Extracting semiconductor device model parameters

ABSTRACT

The present invention includes a method for extracting semiconductor device model parameters for a device model such as the BSIM4 model. The device model parameters for the device model includes a plurality of base parameters, DC model parameters, temperature dependent related parameters, and AC parameters. The method also includes steps for extracting various DC model parameters. The present invention also includes a method for extracting device model parameters including the steps of extracting a portion of the DC model parameters based on the terminal current data, modifying the terminal current data based on the extracted portion of the DC model parameters, and extracting a second portion of the DC model parameters based on the modified terminal current data.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to computer-aided electronic circuit simulation, and more particularly, to a method of extracting semiconductor device model parameters for use in integrated circuit simulation.

2. Description of Related Art

Computer aids for electronic circuit designers are becoming more prevalent and popular in the electronic industry. This move toward electronic circuit simulation was prompted by the increase in both complexity and size of circuits. As circuits have become more complex, traditional breadboard methods have become burdensome and overly complicated. With increased computing power and efficiency, electronic circuit simulation is now standard in the industry. Examples of electronic circuit simulators include the Simulation Program with Integrated Circuit Emphasis (SPICE) developed at the University of California, Berkeley (UC Berkeley), and various enhanced versions or derivatives of SPICE, such as, SPICE2 or SPICE3, also developed at UC Berkeley; HSPICE, developed by Meta-software and now owned by Avant!; PSPICE, developed by Micro-Sim; and SPECTRE, developed by Cadence. SPICE and its derivatives or enhanced versions will be referred to hereafter as SPICE circuit simulators.

SPICE is a program widely used to simulate the performance of analog electronic systems and mixed mode analog and digital systems. SPICE solves sets of non-linear differential equations in the frequency domain, steady state and time domain and can simulate the behavior of transistor and gate designs. In SPICE, any circuit is handled in a node/element fashion; it is a collection of various elements (resistors, capacitors, etc.). These elements are then connected at nodes. Thus, each element must be modeled to create the entire circuit. SPICE has built in models for semiconductor devices, and is set up so that the user need only specify model parameter values.

An electronic circuit may contain any variety of circuit elements such as resistors, capacitors, inductors, mutual inductors, transmission lines, diodes, bipolar junction transistors (BJT), junction field effect transistors (JFET), and metal-on-silicon field effect transistors (MOSFET), etc. A SPICE circuit simulator makes use of built-in or plug-in models for semiconductor device elements such as diodes, BJTs, JFETs, and MOSFETs. If model parameter data is available, more sophisticated models can be invoked. Otherwise, a simpler model for each of these devices is used by default.

A model for a device mathematically represents the device characteristics under various bias conditions. For example, for a MOSFET device model, in DC and AC analysis, the inputs of the device model are the drain-to-source, gate-to-source, bulk-to-source voltages, and the device temperature. The outputs are the various terminal currents. A device model typically includes model equations and a set of model parameters. The model parameters, along with the model equations in the device model, directly affect the final outcome of the terminal currents. In order to represent actual device performance, a successful device model is tied to the actual fabrication process used to manufacture the device represented. This connection is represented by the model parameters, which are dependent on the fabrication process used to manufacture the device.

SPICE has a variety of preset models. However, in modern device models, such as BSIM (Berkeley Short-Channel IGFET Model) and its derivatives, BSIM3, BSIM4, and BSIMPD (Berkeley Short-Channel IGFET Model Partial Depletion), all developed at UC Berkeley, only a few of the model parameters can be directly measured from actual devices. The rest of the model parameters are extracted using nonlinear equations with complex extraction methods. See Daniel Foty, “MOSFET Modeling with Spice—Principles and Practice,” Prentice Hall PTR, 1997.

Since the sets of equations utilized in a modern semiconductor device model are complex with numerous unknowns, there is a need to extract the model parameters in the equations in an efficient and accurate manner so that using the extracted parameters, the model equations will closely emulate the actual process.

SUMMARY OF THE INVENTION

The present invention includes a method for extracting semiconductor device model parameters for a device model such as the BSIM4 model. The device model parameters for the device model includes a plurality of base parameters, DC model parameters, temperature dependent related parameters, and AC parameters. The method includes steps for extracting the DC model parameters, such of V_(th) related parameters, I_(gb) related parameters, I_(gidl) related parameters, I_(gd) and I_(gs) related parameter, L_(eff), R_(d) and R_(s) related parameters, mobility and W_(eff) related parameters, V_(th) geometry related parameters, sub-threshold region related parameters, drain induced barrier lower related parameters; I_(dsat) related parameters, and additional DC related parameters, based on the terminal current data corresponding to various bias conditions measured from a set of test devices.

The present invention also includes a method for extracting device model parameters including the steps of extracting a portion of the DC model parameters based on the terminal current data, modifying the terminal current data based on the extracted portion of the DC model parameters, and extracting a second portion of the DC model parameters based on the modified terminal current data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a system according to an embodiment of the present invention;

FIG. 2 is a flow chart illustrating a modeling process in accordance with an embodiment of the present invention;

FIG. 3A is a block diagram of a model definition input file in accordance with an embodiment of the present invention;

FIG. 3B is a block diagram of an object definition input file in accordance with an embodiment of the present invention;

FIG. 4 is a diagrammatic cross sectional view of a MOSFET device for which model parameters are extracted in accordance with an embodiment of the present invention;

FIG. 5 is a graph illustrating sizes of test devices used to obtain experimental data for model parameter extraction in accordance with an embodiment of the present invention;

FIG. 6 is a graph illustrating sizes of test devices used to obtain experimental data for model parameter extraction in accordance with an alternative embodiment of the present invention;

FIGS. 7A-7D are examples of current-voltage (I-V) curves representing some of the terminal current data for the test devices;

FIG. 8 is a flow chart illustrating in further detail a parameter extraction process in accordance with an embodiment of the present invention; and

FIG. 9 is a flow chart illustrating in further detail a DC parameter extraction process in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

As shown in FIG. 1, system 100, according to one embodiment of the invention, comprises a central processing unit (CPU) 102, which includes a RAM, and a disk memory 110 coupled to the CPU 102 through a bus 108. The system 100 further comprises a set of input/output (I/O) devices 106, such as a keypad, a mouse, and a display device, also coupled to the CPU 102 through the bus 108. The system 100 may further include an input port 104 for receiving data from a measurement device (not shown), as explained in more detail below. The system 100 may also include other devices 122. An example of system 100 is a Pentium 233 PC/Compatible computer having RAM larger than 64 MB and a hard disk larger than 1 GB.

Memory 110 has computer readable memory spaces such as database 114 that stores data, memory space 112 that stores operating system 112 such as Windows 95/98/NT4.0/2000, which has instructions for communicating, processing, accessing, storing and searching data, and memory space 116 that stores program instructions (software) for carrying out the method of the present invention. Memory space 116 may be further subdivided as appropriate, for example to include memory portions 118 and 120 for storing modules and plug-in models, respectively, of the software.

A set of model parameters for a semiconductor device is often referred to as a model card for the device. Together with the model equations, the model card is used by a circuit simulator to emulate the behavior of the semiconductor device in an integrated circuit. A model card may be determined by process 200 as shown in FIG. 2. Process 200 begins by loading 210 the input files into the RAM of the CPU 102. The input files may include a model definition file and an object definition file. The object definition file provides information of the object (device) to be simulated. The model definition file provides information associated with the device model for modeling the behavior of the object. These files are discussed in further detail below in conjunction with FIGS. 3A and 3B.

Next, the measurement data is loaded 220 from database 114. The measurement data includes physical measurements from a set of test devices, as will be explained in more detail below. Once the data has been loaded, the next step is extraction 230 of the model parameters. The parameter extraction step 230 is discussed in detail in connection with FIGS. 8, and 9 below.

After the parameters are extracted, binning 240 may be performed. Binning is an optional step depending on whether the device model is binnable or not. The next step is verification 250. Verification checks the quality of the extracted model parameters. Once verified, the extracted parameters are output 260 as model card, an error report is generated 270, and the process 200 is then complete. More detailed discussion about the binning step 240 and verification step 250 can be found in the BSIMPro+User Manual—Basic Operation, by Celestry Design Technologies, released in September, 2001, which is incorporated by reference in its entirety herein.

Referring to FIG. 3A, model definition file 300A comprises a general model information field 310, a parameter definition field 320, an intermediate variable definition field 330, and an operation point definition field 340. The general model information field 310 includes general information about the device model, such as model name, model version, compatible circuit simulators, model type and binning information. The parameter definition field 320 defines the parameters in the model. As an example, a list of the model parameters in the BSIM4 model are provided in Appendix A. For each parameter, the model definition file specifies information associated with the parameter, such as parameter name, default value, parameter unit, data type, and optimization information. The operation point definition section 340 defines operation point or output variables, such as device terminal currents, threshold voltage, etc., used by the model.

Referring to FIG. 3B, object definition file 300B defines object related information, including input variables 350, output variables 360, instance variables 370, object and node information 380. Input variables 350 and output variables 360 are associated with the inputs and outputs, respectively, of the device in an integrated circuit. The instance variables 370 are associated with the geometric characteristics of the device to be modeled. The object node information 380 is the information regarding the nodes or terminals of the device to be modeled.

Process 200 can be used to generate model cards for models describing semiconductor devices such as BJTs, JFETs, and MOSFETs, etc. Discussions about the use of some of these models can be found in the BSIMPro+User Manual—Device Modeling Guide, by Celestry Design Technologies, released in September, 2001, which is incorporated by reference in its entirety herein. As an example, the BSIM4 model, which was developed by UC Berkeley to model MOSFET devices, is used here to further describe the parameter extraction step 230 of the process 200. The model equations for the BSIM4 model are provided in Appendix B. More detailed discussion about the BSIM4 model can be found in the BSIM4.2.0 MOSFET Model Users' Manual by the Department of Electrical Engineering and Computer Sciences, UC Berkeley, Copyright 2001, which is incorporated by reference in its entirety herein.

Preferred embodiments of the present invention, thus may be further understood by reference to an exemplary parameter extraction process for a MOSFET device. As shown in FIG. 4, a MOSFET device 400 includes a source 430 and a drain 450 formed in a substrate 440. The MOSFET also includes a gate 410 over the substrate 440 and is separated from the substrate 440 by a thin layer of gate oxide 420.

The MOSFET as described can be considered a four terminal (node) device. The four terminals are the gate terminal (node g), the source terminal (node s), the drain terminal (node d), and the substrate or body terminal (node b). Nodes g, s, b, and d, can be connected to different voltage sources.

For ease of further discussion, Table I below lists the symbols corresponding to the physical variables associated with the operation of MOSFET device 400. TABLE I C_(bd) - body to drain capacitance C_(bS) - body to source capacitance I_(d) - current through drain (d) node I_(dgidl) - gate induced leakage current at the drain I_(ds) - current flowing from source to drain I_(dsat) - drain saturation current I_(b) - current through substrate node I_(gb) - gate oxide tunneling current to substrate I_(gs) - current flowing from gate to source I_(gd) - current flowing from gate to drain I_(gc) - current flowing from gate to channel I_(sub) - impact ionization current I_(s) - current through source (s) node L_(gisl) - gate induced source leakage current at the source L_(drawn) - drawn channel length L_(eff) - effective channel length R_(d) - drain resistance R_(s) - source resistance R_(ds) - drain/source resistance R_(out) - output resistance V_(bs) - voltage between node b and node s V_(d) - drain voltage V_(DD) - maximum operating DC voltage V_(ds) - voltage between node d and node s V_(b) - substrate voltage V_(g) - gate voltage V_(gs) - voltage between node g and node s V_(s) - source voltage V_(th) - threshold voltage W_(drawn) - drawn channel width W_(eff) - effective channel width

In order to model the behavior of the MOSFET device 400 using the BSIM4 model, experimental data are used to extract model parameters associated with the model. These experimental data include terminal current data and capacitance data measured in test devices under various bias conditions. In one embodiment of the present invention, the measurement is done using a conventional semiconductor device measurement tool that is coupled to system 100 through input port 104. The measured data are thus organized by CPU 102 and stored in database 114. The test devices are typically manufactured using the same or similar process technologies for fabricating the MOSFET device. In one embodiment of the present invention, a set of test devices having different device sizes, meaning different channel widths and channel lengths are used for the measurement. The device size requirement can vary with different applications. Ideally, as shown in FIG. 5, the set of devices include:

-   -   one largest device, meaning the device with the longest drawn         channel length and widest drawn channel width that is available,         as represented by dot 502;     -   one smallest device, meaning the device with the shortest drawn         channel length and smallest drawn channel width that is         available, as represented by dot 516;     -   one device with the smallest drawn channel width and longest         drawn channel length, as represented by dot 510;     -   one device with the widest drawn channel length and shortest         drawn channel length, as represented by dot 520;     -   three devices having the widest drawn channel width and         different drawn channel lengths, as represented by dots 504,         506, and 508;     -   two devices with the shortest drawn channel length and different         drawn channel widths, as represented by dots 512 and 514;     -   two devices with the longest drawn channel length and different         drawn channel widths, as represented by dots 522 and 524;     -   (optionally) up to three devices with smallest drawn channel         width and different drawn channel lengths, as represented by         dots 532, 534, and 536; and     -   (optionally) up to three devices with medium drawn channel width         (about halfway between the widest and smallest drawn channel         width) and different drawn channel lengths, as represented by         dots 538, 540, and 542.         If in practice, it is difficult to obtain measurements for all         of the above required devices sizes, a smaller set of different         sized devices can be used. For example, the different device         sizes shown in FIG. 6 are sufficient according to an alternative         embodiment of the present invention. The test devices as shown         in FIG. 6 include:     -   one largest device, meaning the device with the longest drawn         channel length and widest drawn channel width, as represented by         dot 502;     -   one smallest device, meaning the device with the shortest drawn         channel length and smallest drawn channel width, as represented         by dot 516;     -   (optional) one device with the smallest drawn channel width and         longest drawn channel length, as represented by dot 510;     -   one device with the widest drawn channel width and shortest         drawn channel length, as represented by dot 520;     -   one device and two optional devices having the widest drawn         channel width and different drawn channel lengths, as         represented by dots 504 (optional), 506 (optional), and 508,         respectively;     -   (optional) two devices with the shortest drawn channel length         and different drawn channel widths, as represented by dots 512         and 514.

For each test device, terminal currents are measured under different terminal bias conditions. These terminal current data are put together as I-V curves representing the I-V characteristics of the test device. In one embodiment of the present invention, for each test device, the following I-V curves are obtained:

-   -   1. Linear region I_(d) vs. V_(gs) curves for a set of V_(b)         values. These curves are obtained by grounding the s node,         setting V_(d) to a low value, such as 0.05V, and for each of the         set of V_(b) values, measuring I_(d) while sweeping V_(g) in         step values across a range such as from 0 to V_(DD). (−V_(DD)         for NMOS _(and) V_(DD) for PMOS).     -   2. Saturation region I_(d) vs. V_(gs) curves for a set of V_(b)         values. These curves are obtained by grounding the s node,         setting V_(d) to a high value, such as V_(DD), and for each of         the set of V_(b) values, measuring I_(d) while sweeping V_(g) in         step values across a range such as from 0 to V_(DD). (−V_(DD)         for NMOS _(and) V_(DD) for PMOS).     -   3. Saturation region I_(d) VS V_(ds) curves for a set of V_(g)         values. These curves are obtained by grounding the s node,         setting V_(b) to 0 and for each set of V_(g) values, measuring         I_(d) while sweeping V_(d) in step values across a range such as         V_(th)+0.02 to V_(DD).     -   4. Linear region I_(d) vs V_(ds) curves for a set of V_(g)         values with substrate biased. These curves are obtained by         grounding the s node, setting V_(b) to −V_(DD) and for each set         of V_(g) values, measuring I_(d) while sweeping V_(d) in step         values across a range such as V_(th)+0.02 to V_(DD).     -   5. I_(b) vs. V_(gs) curves for different V_(d) values, obtained         by grounding the s and b nodes, and for each of the set of V_(d)         values, measuring I_(b) while sweeping V_(g) in step values         across a range such as from 0 to V_(DD).     -   6. I_(g) vs. V_(bs) curves obtained by grounding d, g, and s         nodes, measuring I_(g) while sweeping V_(b) in step values         across a range such as from −V_(DD) to 0.7.     -   7. I_(g)/I_(d)/I_(s) vs. V_(gs) curves for different V_(d)         values, obtained by grounding s and b nodes, and for each of a         set of V_(d) values sweeping V_(g) in step values across a range         such as from 0 to V_(DD).     -   8. I_(s) vs. V_(gd) curves for different V_(b) and V_(s) values,         obtained by grounding d node, and for each combination of V_(b),         and V_(s) values, measuring I_(s) while sweeping V_(g) in step         values across a range such as from 0 to −V_(DD).

As examples, FIG. 7A shows a set of linear region I_(d) vs. V_(gs) curves for different V_(bs) values, FIG. 7B shows a set of saturation region I_(d) vs. V_(ds) curves for different V_(gs) values, FIG. 7C shows a set of I_(g) vs. V_(gs) curves for different V_(ds) values; and FIG. 7D shows a set of I_(g) vs. V_(gs) curves for different V_(bd) values.

In addition to the terminal current data, for each test device, capacitance data are also collected from the test devices under various bias conditions. The capacitance data can be put together into capacitance-current (C-V) curves. In one embodiment of the present invention, the following C-V curves are obtained:

-   1. C_(bs) VS. V_(bs) curve obtained by grounding s node, setting     I_(d) to zero, or to very small values, and measuring C_(bs) while     sweeping V_(b) in step values across a range such as from −V_(DD) to     V_(DD). -   2. C_(bd) vs. V_(bs) curve obtained by grounding s node, setting     I_(s) to zero, or to very small values, and measuring C_(bd) while     sweeping V_(b) in step values across a range such as from −V_(DD) to     V_(DD).

As shown in FIG. 8, in one embodiment of the present invention, the parameter extraction step 230 comprises extracting base parameters 810; extracting other DC model parameters 820; extracting temperature dependent related parameters 830; and extracting AC parameters 840. In base parameters extraction step 810, base parameters, such as V_(th) (the threshold voltage at V_(bs)=0), K₁ (the first order body effect coefficient), and K₂ (the second order body effect coefficient) are extracted based on process parameters corresponding to the process technology used to fabricate the MOSFET device to be modeled. The base parameters are then used to extract other DC model parameters at step 820, which is explained in more detail in connection with FIG. 9 below.

The temperature dependent parameters are parameters that may vary with the temperature of the device and include parameters such as: Kt1 (temperature coefficient for threshold voltage); Ua1 (temperature coefficient for U_(a)), and Ub1 (temperature coefficient for U_(b)), etc. These parameters can be extracted using a conventional parameter extraction method.

The AC parameters are parameters associated with the AC characteristics of the MOSFET device and include parameters such as: CLC (constant term for the short channel model) and moin (the coefficient for the gate-bias dependent surface potential), etc. These parameters can also be extracted using a conventional parameter extraction method.

As shown in FIG. 9, the DC parameter extraction step 820 further comprises: extracting V_(th) related parameters (step 902); extracting I_(gb) related parameters (step 904); extracting I_(gidl) related parameters (step 906); extracting I_(gd) and I_(gs) related parameters (step 908); extracting I_(gc) and its partition (I_(gcs) and I_(gcd)) related parameters (step 910); extracting L_(eff) related parameters, R_(d) related parameters, and R_(s) related parameters (step 912); extracting mobility related parameters and W_(eff) related parameters (step 914); extracting V_(th) geometry related parameters (step 916); extracting sub-threshold region related parameters (step 918); extracting parameters related to drain-induced barrier lower than regular (DIBL) (step 920); extracting I_(dsat) related parameters (step 922); extracting I_(sub) related parameters (step 924); and extracting junction parameters (step 926).

The equation numbers below refer to the equations set forth in Appendix B.

In step 902, threshold voltage V_(th) related parameters, such as V_(th0), k1, k2, and Ndep, are extracted by using the linear I_(d) vs V_(gs) curves measured from the largest device.

In step 904, the tunneling current, Igb, related parameters are extracted. The tunneling current is comprised of two components as defined by the following equation: I _(gb) =Igbacc+Igbinv

Igbacc and Igbinv related parameters are extracted separately in step 904. For the extraction of Igbacc related parameters, the I_(g) vs. V_(bs) curves for V_(ds)=0 and V_(gs)=0 are used. V_(ds) and V_(gs) are set to zero to minimize the effects of other currents. Then model parameters Aigbacc, Bigbacc, and Cigbacc are extracted with nonlinear-square-fit, using Equation 4.3.1. Once these parameters are extracted, Nigbacc is obtained by linear interpolation of Equation 4.3.1b using maximum slope position in the I_(g) vs. V_(bs) curves.

For the extraction of Igbinv related parameters, the I_(b) vs. V_(gs) curves when V_(ds)=0 and V_(bs)=0 are used. V_(ds) and V_(bs) are set to zero to minimize the effects of other currents. Model parameters Aigbinv, Bigbinv, Cigbinv are then extracted with nonlinear-square-fit, using Equation 4.3.2. Then Nigbinv and Eigbinv are obtained using Equation 4.3.2a by conventional optimization methods such as the Newton-Raphson algorithm.

In step 906, I_(gidl)-related parameters, such as parameters AGIDL, BGIDL, CGIDL, and EGIDL, are extracted. I_(gidl) represents the gate-induced drain leakage current, and the parameters are extracted using the device with the maximum width, W, and data from the I_(d) VS V_(gs) and I_(s) vs V_(gs) curves measured at the condition of V_(gs)<0 for NMOS (V_(gs)>0 for PMOS) and at different V_(ds) and V_(bs) bias conditions. I_(sub) is negligible where V_(gs)<0 and therefore the I_(b) vs V_(gs) curve can be used for this extraction. These assumptions and curves are used in conjunction with the extracted V_(th), related parameters from step 902 and the following equation: $\begin{matrix} {I_{GIDL} = {{AGIDL} \cdot W_{effCJ} \cdot {Nf} \cdot \frac{V_{ds} - V_{gse} - {EGIDL}}{3 \cdot T_{oxe}} \cdot}} \\ {{\exp\left( {- \frac{3 \cdot T_{oxe} \cdot {BGIDL}}{V_{ds} - V_{gse} - {EGIDL}}} \right)} \cdot \frac{V_{db}^{3}}{{CGIDL} + V_{db}^{3}}} \end{matrix}$ CGIDL is extracted using the I_(b) vs V_(gs) curve data for varying V_(ds). Next AIGDL and BIGDL are extracted using a conventional non-linear square fit. Finally EGIDL is obtained by optimizing AGIDL, BGIDL, and EGIDL simultaneously using a conventional optimizer such as the Newton-Raphson algorithm.

In step 908, the gate to source, I_(gs), and gate to drain, I_(gd) current parameters are extracted. I_(gs) represents the gate tunneling current between the gate and the source diffusion region, I_(gd) represents the gate tunneling current between the gate and the drain diffusion region. Parameters extracted in step 908 include DLCIG, AIGSD, BIGSD, and CIGSD. The values of the parameters POXEDGE, TOXREF, and NTOX are set to their default values. These parameters are extracted using the I_(d) vs V_(gs) and I_(s) vs V_(gs) curves measured at the condition of V_(ds)=0 and V_(bs)=0. V_(ds) and V_(bs) are set equal to zero to minimize the effects of other currents such as channel current. This extraction utilizes the device with the maximum L_(drawn)*W_(drawn), where L_(drawn) is the device channel length and W_(drawn) is the device width, and the extracted V_(th), related parameters from step 902.

The following equations are utilized: I _(gs) =W _(eff) DLCIG·A·T _(oxRatioEdge) ·V _(gs) ·V′ _(gs) ·exp[−B·TOXE·POXEDGE·(AIGSD−BIGSD·V′ _(gs))·(1+CIGSD·V′ _(gs))] and I _(gd) =W _(eff) DLCIG·A·T _(oxRatioEdge) ·V _(gd) ·V′ _(gd) ·exp[−B·TOXE·POXEDGE·(AIGSD−BIGSD·V′ _(gd))·(1+CIGSD·V′ _(gd))] where $T_{oxRatioEdge} = {\left( \frac{TOXREF}{{TOXE} \cdot {POXEDGE}} \right)^{NTOX} \cdot \frac{1}{\left( {{TOXE} \cdot {POXEDGE}} \right)^{2}}}$ and V′ _(gs){square root}{square root over ((V _(gs) −V _(fbsd))²+1.0e−4)} V _(gd)={square root}{square root over ((V _(gd) −V _(fbsd))²+1.0e−4)} DLCIG is set equal to 0.7 *X_(j) which is a proven experimental value. Then AIGSD, BIGSD, and CIGSD are extracted from the I_(d)/I_(s) vs V_(gs) curve using the non-linear square fit method.

In step 910, the gate to current, I_(gc), and it's partition related parameters are extracted. Parameters extracted in step 910 includes: AIGC, BIGC, CIGC, NIGC and P_(igcd). These parameters are extracted using the device with the maximum L_(drawn)*W_(drawn) and the data from the I_(g) vs V_(gs) curve measured at the condition of V_(ds)=0 and V_(bs)=0. V_(ds) and V_(bs) are set equal to zero to minimize the effects of other currents such as channel current. The data of I_(g) includes I_(gc), I_(gs) and I_(gd) data and is characterized by the following equation. I _(g) =I _(gc) +I _(gs) +I _(gd) Since I_(gs) and I_(gd) are extracted in earlier steps, these effects can easily be removed with the calculated I_(gs) and I_(gd). I_(gc) is then calculated using the extracted V_(th), related parameters from step 902, in coordination data from the I_(g) vs V_(gs) curve and the following equation: I _(gc) =W _(eff) L _(eff) ·A·T _(oxRatio) ·V _(gse) V _(aux) ·exp[−B·TOXE(AIGC−BIGC·V _(oxdepinv))·(1+CIGC·V _(oxdepinv))] Where $V_{aux} = {{NIGC} \cdot v_{t} \cdot {\log\left( {1 + {\exp\left( \frac{V_{gse} - {VTH0}}{{NIGC} \cdot v_{t}} \right)}} \right)}}$ Using a non-linear square fit, AIGC, BIGC, and CIGC are extracted. NIGC is then extracted at V_(gs)=V_(th0) using linear interpolation.

Once calculated, Igc is then divided into its two components I_(gcs) and I_(gcd) $\begin{matrix} {I_{gcs} = {I_{gc} \cdot \frac{{{PIGCD} \cdot V_{ds}} + {\exp\left( {{- {PIGCD}} \cdot V_{ds}} \right)} - 1 + {1.0e} - 4}{{{PIGCD}^{2} \cdot V_{ds}^{2}} + {2.0e} - 4}}} \\ {I_{\gcd} = {I_{gc} \cdot \frac{1 - {\left( {{{PIGCD} \cdot V_{ds}} + 1} \right) \cdot {\exp\left( {{- {PIGCD}} \cdot V_{ds}} \right)}} + {1.0e} - 4}{{{PIGCD}^{2} \cdot V_{ds}^{2}} + {2.0e} - 4}}} \end{matrix}$ and

In step 912, parameters related to the effective channel length L_(eff), the drain resistance R_(d) and source resistance R_(s) are extracted. The L_(eff), R_(d) and R_(s) related parameters include parameters such as L_(int), and R_(dsw), and are extracted using data from the linear I_(d) vs V_(gs) curves as well as the extracted V_(th) related parameters from step 902.

In step 914, parameters related to the mobility and effective channel width W_(eff), such as μ₀, U_(a), U_(b), U_(c), Wint, Wr, Prwb, Wr, Prwg, R_(dsw), Dwg, and Dwb, are extracted, using the linear I_(d) VS V_(gs) curves and the extracted V_(th), related parameters from step 902.

Steps 902, 912, and 914 can be performed using a conventional BSIM4 model parameter extraction method. Discussions about some of the parameters involved in these steps can be found in the following:

-   -   Liu, William “MOSFET Models for SPICE Simulation, Including         BSIM3v3 and BSIM4,” John Wiley & Sons, Inc. 2001         which is incorporated by reference herein.

In step 916, the threshold voltage V_(th) geometry related parameters, such as D_(VT0), D_(VT1), D_(VT2), N_(LX1), D_(VT0W), D_(VT1W), D_(VT2W), k₃, and k_(3b), are extracted, using the linear I_(d) vs V_(gs) curve, the extracted V_(th), L_(eff), and mobility and W_(eff) related parameters from steps 902, 912, and 914, and Equations 2.5.5-2.5.7.

In step 918, sub-threshold region related parameters, such as C_(it), Nfactor, V_(off), D_(dsc), and C_(dscd), are extracted, using the linear I_(d) vs V_(gs) curves, the extracted V_(th), L_(eff) and R_(d) and R_(s) and mobility and W_(eff) related parameters from steps 902, 912, and 914, and Equations (3.2.1-3.2.3.

In step 920, DIBL related parameters, such as D_(sub), Eta0 and Etab, are extracted, using the saturation I_(d) vs V_(gs) curves and the extracted V_(th) related parameters from step 902, and Equations 2.5.5-2.5.7.

In step 922, the drain saturation current I_(dsat) related parameters, such as B0, B1, A0, Keta, and A_(gs), are extracted using the saturation I_(d) VS V_(ds) curves, the extracted V_(th), L_(eff) and R_(d) and R_(s), mobility and W_(eff), V_(th) geometry, sub-threshold region, and DIBL related parameters from steps 902, 912, 914, 916, 918, and 920 and Equation 14.1.

In step 924, the impact ionization current I_(ii) related parameters, such as α₀, α₁, and β₀, are extracted using the data from the linear I_(d) VS V_(gs) curve and Equations 6.1.1-6.1.2.

In step 926, the junction parameters, such as Cjswg, Pbswg, and Mjswg, are extracted using the C_(bs) VS. V_(bs) and C_(bd) vs. V_(bs) curves, and Equations 10.2.1-10.2.7.

In performing the DC parameter extraction steps (steps 902-926), it is preferred that after the I_(gb), I_(gd), I_(gs) I_(gidl), and I_(gc) related parameters are extracted in steps 904 through 910, I_(gb), I_(gd), I_(gs), I_(gidl), and I_(gc) are calculated based on these parameters and the model equations. This calculation is done for the bias condition of each data point in the measured I-V curves. The I-V curves are then modified for the first time based on the calculated I_(gb), I_(gd), I_(gs), I_(gidl), and I_(gc) values. In one embodiment of the present invention, the I-V curves are first modified by subtracting the calculated I_(gb), I_(gd), I_(gs), I_(gidl), and I_(gc) values from respective I_(s), I_(d), and I_(b) data values. For example, for a test device having drawn channel length L_(drn) and drawn channel width W_(drn), if under bias condition where V_(s)=V_(s) ^(T), V_(d)=V_(d) ^(T), V_(p)=V_(p) ^(T), V_(e)=V_(e) ^(T), and V_(g)=V_(g) ^(T), the measured drain current is I_(d) ^(T), then after the first modification, the drain current will be I_(d) ^(first-modified)=I_(d) ^(T)−I_(gd) ^(T)−I_(gidl) ^(T) where I_(gd) ^(T) and I_(gidl) ^(T), are calculated respectively, for the same test device under the same bias condition. The first-modified I-V curves are then used for additional DC parameter extraction. This results in higher degree of accuracy in the extracted parameters. In one embodiment the I_(gb), I_(gd), I_(gs), I_(gidl) and I_(gc) related parameters are extracted before extracting other DC parameters, so that I-V curve modification may be done for more accurate parameter extraction. However, if such accuracy is not required, one can choose not to do the above modification and the I_(gb), I_(gd), I_(gs), I_(gidl), and I_(gc) related parameters can be extracted at any point in the DC parameter extraction step 820.

The forgoing descriptions of specific embodiments of the present invention are presented for purpose of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, obviously many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. Furthermore, the order of the steps in the method are not necessarily intended to occur in the sequence laid out. It is intended that the scope of the invention be defined by the following claims and their equivalents. APPENDIX A Parameter List Parameter Default name Description value Binnable? Note A.1 BSIM 4.0.0 Model Selectors/Controllers (LEVEL SPICE3 model selector 14 NA BSIM4 SPICE3 also set as parameter) the default model in SPICE3 VERSION Model version number 4.0.0 NA Berkeley Latest official release BINUNIT Binning unit selector 1 NA — PARAMCHK Switch for parameter value check 1 NA Parameters checked MOBMOD Mobility model selector 0 NA — RDSMOD Bias-dependent source/drain 0 NA R_(ds)(V) resistance model selector modeled internally through IV equation IGCMOD Gate-to-channel tunneling current 0 NA OFF model selector IGBMOD Gate-to-substrate tunneling current 0 NA OFF model selector CAPMOD Capacitance model selector 2 NA — RGATEMOD Gate resistance model selector 0 (Also an (no gate instance resistance) parameter) RBODYMOD Substrate resistance network model 0 NA — (Also an selector (network instance off) parameter) TRNQSMOD Transient NQS model selector 0 NA OFF (Also an instance parameter) ACNQSMOD AC small-signal NQS model 0 NA OFF (Also an selector instance parameter) FNOIMOD Flicker noise model selector 1 NA — TNOIMOD Thermal noise model selector 0 NA — DIOMOD Source/drain junction diode IV 1 NA — model selector PERMOD Whether PS/PD (when given) 1 NA — includes the gate-edge perimeter (including the gate- edge perimeter) GEOMOD Geometry-dependent parasitics 0 NA — (Also an model selector - specifying how the (isolated) instance end S/D diffusions are connected parameter) RGEOMOD Source/drain diffusion resistance 0 NA — (Instance and contact model selector - (no S/D parameter specifying the end S/D contact type: diffusion only) point, wide or merged, and how resistance) S/D parasitics resistance is computed A.2 Process Parameters EPSROX Gate dielectric constant relative to 3.9 (SiO₂) No Typically vacuum greater than or equal to 3.9 TOXE Electrical gate equivalent oxide 3.0e−9m No Fataleno thickness r if not positive TOXP Physical gate equivalent oxide TOXE No Fatalerro thickness r if not positive TOXM Tox at which parameters are extracted TOXE No Fatal error if not positive DTOX Defined as (TOXE-TOXP) 0.0 m No — XJ S/D junction depth 1.5e−7m Yes — GAMMA1 Body-effect coefficient near the surface calculated V^(1/2) Note-1 (λ1 in calculated equation) GAMMA2 Body-effect coefficient in the bulk calculated V^(1/2) Note-1 (λ1 in equation) NDEP Channel doping concentration at 1.7e17cm⁻3 Yes Note-2 depletion edge for zero body bias NSUB Substrate doping concentration 6.0e16cm⁻3 Yes — NGATE Poly Si gate doping concentration 0.0 cm⁻³ Yes — NSD Source/drain doping concentrationFatal 1.0e20cm⁻³ Yes — error if not positive VBX V_(b s) at which the depletion region calculated No Note-3 width equalsXT (V) XT Doping depth 1.55e−7m Yes — RSH Source/drain sheet resistance 0.0 ohm/ No Should square not be negative RSHG Gate electrode sheet resistance 0.1 ohm/ No Should square not be negative A.3 Basic Model Parameters VTH0 or Long-channel threshold voltage at 0.7 V Yes Note-4 VTHO V_(bs) = 0 (NMOS) −0.7 V (PMOS) VEB Flat-band voltage −1.0 V Yes Note-4 PHLN Non-uniform vertical doping effect on 0.0 V Yes — surface potential K1 First-order body bias coefficient 0.5 V^(1/2) Yes Note-5 K2 Second-order body bias coefficient 0.0 Yes Note-5 K3 Narrow width coefficient 80.0 Yes − K3B Body effect coefficient of K3 0.0 V⁻¹ Yes — W0 Narrow width parameter 2.5e−6m Yes — LPE0 Lateral non-uniform doping parameter 1.74e−7m Yes — at V_(bS) = 0 LPEB Lateral non-uniform doping effect on 0.0 m Yes — K1 VBM Maximum applied body bias in VTHO −3.0 V Yes — calculation DVT0 First coefficient of short-channel effect 2.2 Yes — on V_(th) DVT1 Second coefficient of short-channel 0.53 Yes — effect on ^(V)th DVT2 Body-bias coefficient of short-channel −0.032 V ⁻¹ Yes — effect on Vth DVTPO First coefficient of drain-induced V_(th) 0.0 m Yes Not shift due to for long-channel pocket modeled binned devices if binned DVTPO <=0.0 DVTP1 First coefficient of drain-induced Vth 0.0 V⁻¹ Yes — chist due to for long-channel pocket devices Basic Model Parameters DVT0W First coefficient of narrow width effect 0.0 Yes — on V_(th) for small channel length DVT1W Second coefficient of narrow width 5.3e6m⁻¹ Yes — effect on V_(th) for small channel length DVT2W Body-bias coefficient of narrow width −0.032 V⁻¹ Yes effect for small channel length U0 Low-field mobility 0.067 Yes — m²/(Vs) (NMOS); 0.025 m²/(Vs) PMOS UA Coefficient of first-order mobility 1.0e−9 m/V Yes — degradation due to vertical field for MOBMOD = 0 and 1; 1.0e−15 m/V for MOBMOD = 2 UB Coefficient of secon-order mobility 1.0e−19 m²/V² Yes — degradation due to vertical field UC Coefficient of mobility degradation −0.0465 V⁻¹ Yes — due to body- bias effect for MOB- MOD = 1; −0.0465e−9 m/V² for MOBMOD = 0 and 2 EU Exponent for mobility degradation of 1.67 — MOBMOD = 2 (NMOS); 1.0 (PMOS) VSAT Saturation velocity 8.0e4m/s Yes — A0 Coefficient of channel-length 1.0 Yes — dependence of bulk charge effect AGS Coefficient of V_(gs) dependence of bulk 0.0 V⁻¹ Yes — charge effect B0 Bulk charge effect coefficient for 0.0 m Yes — channel width B1 Bulk charge effect width offset 0.0 m Yes — KETA Body-bias coefficient of bulk charge —0.047 V⁻¹ Yes — effect A1 First non-saturation effect parameter 0.0 V⁻¹ Yes A2 Second non-saturation factor 1.0 Yes — WINT Channel-width offset parameter 0.0 m No — LINT Channel-length offset parameter 0.0 m No — DWG Coefficient of gate bias dependence of 0.0 m/V Yes — W_(eff) DWB Coefficient of body bias dependence of 0.0 m/V^(1/2) Yes — W_(eff) VOFF Offset voltage in subtbreshold −0.08 V Yes — region for large W and L VOFFL Channel-length dependence of VOFF 0.0 mV No — MINV V_(gsteff) fitting parameter for moderate 0.0 Yes — inversion condition NFACTOR Subthreshold swing factor 1.0 Yes — ETA0 DIBL coefficient in subthreshold region 0.08 Yes — ETAB Body-bias coefficient for the −0.07 V⁻¹ Yes — subthreshold DTBL effect DSUB DIBL coefficient exponent in DROUT Yes — subthreshold region CIT Interface trap capacitance 0.0 F/m² Yes — CDSC coupling capacitance between 2.4e−4F/m² Yes — source/drain and channel CDSCB Body-bias sensitivity of Cdsc 0.0F/(Vm²) Yes — CDSCD Drain-bias sensitivity of CDSC 0.0(F/Vm²) Yes — PCLM Channel length modulation parameter 1.3 Yes — PDIBLC1 Parameter for DIBL effect on Rout 0.39 Yes — PDIBLC2 Parameter for DIBL effect on Rout 0.0086 Yes — PDIBLCB Body bias coefficient of DIBL effect on 0.0V⁻¹ Yes — Rout DROUT Channel-length dependence of DIBL 0.56 Yes — effect on Rout PSCBE1 First substrate current induced body- 4.24e8Vm Yes — effect parameter PSCBE2 Second substrate current induced body- 1.0e−5m/V Yes — effect parameter PVAG Gate-bias dependence of Early voltage 0.0 Yes — DELTA Parameter for DC V_(dseff) 0.01V Yes — (δ in equation) FPROUT Effect of pocket implant on Rout 0.0 V/m^(0.5) Yes Not degradation modeled if binned FPROUT not positive PDITS Impact of drain-induced V_(th) shift on 0.0 V⁻¹ Yes Not modeled Rout if Rout binned PDITS = 0; Fatal error if binned PDITS negative PDITSL Channel-length dependence of drain- 0.0 m⁻ No Fatal induced V_(th) shift for Rout error if PDITSL negative PDITSD V_(ds) dependence of drain-induced V_(th) Yes — shift for Rout A.4 Parameters for Asymmetric and Bias-Dependent R_(ds) Model RDSW Zero bias LDD resistance per unit width 200.0 Yes If for RDSMOD = 0 ohm negative, (μm)^(WR) reset to 0.0 RDSWMIN LDD resistance per unit width at 0.0 No — high V_(gs) and zero V_(bs) ohm for RDSMOD = 0 (μm)^(WR) RDW Zero bias lightly-doped drain resistance 100.0 Yes — R_(d)(V) per unit width for RDS-MOD = 1 ohm (μm)^(WR) RDWMIN Lightly-doped drain resistance per unit 0.0 No — width at high V_(gs) and zero V_(bs) for ohm RDSMOD = 1 (μm)^(WR) RSW Zero bias lightly-doped source 100.0 Yes — resistance R_(s)(V) per unit ohm width for RDS-MOD = 1 (μm)^(WR) RSWMIN Lightly-doped source resistance per unit 0.0 No — width at high V_(gs) and zero V_(bs) for RDSMOD = 1 PRWG Gate-bias dependence of LDD 1.0 V⁻¹ Yes — resistance PRWB Body-bias dependence of LDD 0.0 V^(−0.5) Yes — resistance WR Channel-width dependence parameter of 1.0 Yes — LDD resistance NRS Number of source diffusion square 1.0 No — (instance parameter only) NRD Number of drain diffusion squares 1.0 No — (instance parameter only) ALPHA0 First parameter of impact ionization 0.0 Am/V Yes — current ALPHA1 Isub parameter for length scaling 0.0 A/V Yes — BETA0 The second parameter of impact 30.0 V Yes — ionization current A.6 Gate-Induced Drain Leakage Model Parameters AGIDL Pre-exponential coefficient for GLDL 0.0 mho Yes I_(gidl) = 0.0 if binned AGIDL = 0.0 BGIDL Exponential coefficient for GIDL 2.3e9 V/m Yes I_(gidl) = 0.0 if binned BGIDL = 0.0 CGIDL Paramter for body-bias effect on GIDL 0.5 V³ Yes — DGIDL Fitting parameter for band bending for 0.8 V Yes — GIDL A.7 Gate Dielectric Tunneling Current Model Parameters AIGBACC Parameter for I_(gb) in accumulation 0.43 Yes — (Fs²/g)^(0.5)m⁻¹ BIGBACC Parameter for I_(gb) in accumulation 0.054 Yes — (Fs²/g)^(0.5) m⁻¹V⁻¹ CIGBACC Parameter for I_(gb) in accumulation 0.075 V⁻¹ Yes — NIGBACC Parameter for I_(gb) in accumulation 1.0 Yes Fatal error if binned value not positive AIGBINV Parameter for I_(gb) in inversion 0.35 Yes — (Fs²/g)^(0.5)m⁻¹ BIGBINV Parameter for I_(gb) in inversion 0.03 Yes — (Fs²/g)^(0.5) CIGBINV Parameter for I_(gb) in inversion 0.006 V⁻¹ Yes — EIGBINV Parameter for I_(gb) in inversion 1.1 V Yes — NIGBINV Parameter for I_(gb) in inversion 3.0 Yes Fatal error if binned value not positive AIGC Parameter for I_(gcs) and I_(gcd) 0.054 Yes — (NMOS) and 0.31 (PMOS) (Fs²/g)^(0.5)m⁻¹ BIGC Parameter for I_(gcs) and I_(gcd) 0.054 Yes — (NMOS) and 0.024 (PMOS) (Fs²/g)^(0.5) m⁻¹V⁻¹ CIGG Parameter for I_(gcs) and I_(gcd) 0.075 Yes — (NMOS) and 0.03 (PMOS) V⁻¹ AIGSD Parameter for I_(gs) and I_(gd) 0.43 Yes — (NMOS) and 0.31 (PMOS) (Fs²/g)^(0.5)m⁻¹ BIGSD Parameter for I_(gs) and I_(gd) 0.054 Yes — (NMOS) and 0.024 (PMOS) (Fs²/g)^(0.5) m⁻¹V⁻¹ CIGSD Parameter for I_(gs) and I_(gd) 0.075 Yes — (NMOS) and 0.03 (PMOS) V⁻¹ DLCIG Source/drain overlap length for I_(gs) LINT Yes — and I_(gd) NIGC Parameter for I_(gcs), I_(gcd), I_(gs) and I_(gd) 1.0 Yes Fatal error if binned value not positive POXEDGE Factor for the gate oxide thickness in 1.0 Yes Fatal error source/drain overlap regions if binned value not positive PIGCD V_(ds) dependence of I_(gcs) and I_(gcd) 1.0 Yes Fatal error if binned value not positive NTOX Exponent for the gate oxide ratio 1.0 Yes — TOXREF Nominal gate oxide thickness for gate 3.0e−9m No Fatal error dielectric tunneling current model if not positive only A.8 Charge and Capacitance Model Parameters XPART Charge partition parameter 0.0 No — CGSO Non LDD region source-gate overlap calculated No Note-6 capacitance per unit channel width (F/m) CGDO Non LDD region drain-gate overlap calculated No Note-6 capacitance per unit channel width (F/m) CGBO Gate-bulk overlap capacitance per 0.0 F/m Note-6 unit channel length CGSL Overlap capacitance between gate and 0.0 F/m Yes — lightly-doped source region CGDL Overlap capacitance between gate and 0.0 F/m Yes — lightly-doped source region CKAPPAS Coefficient of bias-dependent overlap 0.6 V Yes — capacitance for the source side CKAPPAD Coefficient of bias-dependent overlap CKAPPAS Yes — capacitance for the drain side CF Fringing field capacitance calculated Yes Note-7 (F/m) CLC Constant term for the short channel 1.0e−7m Yes — model CLE Exponential term for the short channel 0.6 Yes — model DLC Channel-length offset parameter for LINT (m) No — CV model DWC Channel-width offset parameter for WINT (m) No — CV model VFBCV Flat-band voltage parameter (for —1.0 V Yes — CAPMOD = 0 only) NOFF CV parameter in V_(gsteff,CV) for weak to 1.0 Yes — strong inversion VOFFCV CV parameter in V_(gsteff,CV) for week to 0.0 V Yes — strong inversion ACDE Exponential coefficient for charge 1.0 m/V Yes — thickness in CAPMOD = 2 for accumu- lation and depletion regions MOIN Coefficient for the gate-bias depen- 15.0 Yes — dent surface potential A.9 High-Speed/RF Model Parameters XRCRG1 Parameter for distributed channel- 12.0 Yes Warning resistance effect for both intrinsic- message input resistance and charge-deficit issued if NQS models binned XRCRG1 <=0.0 XRCRG2 Parameter to account for the excess 1.0 Yes — channel diffusion resistance for both intrinsic input resistance and charge- deficit NQS models RBPB Resistance connected between 50.0 ohm No If less than (Also an bNodePrime and bNode 1.0e−3ohm, instance reset to parameter) 1.0e−3ohm RBPD Resistance connected between 50.0 ohm No If less than (Also an bNodePrime and dbNode 1.0e−3ohm, instance reset to parameter) 1.0e−3ohm RBPS Resistance connected between 50.0 ohm No If less than (Also an bNodePrime and sbNode 1.0e−3ohm, instance reset to parameter) 1.0e−3ohm RBDB Resistance connected between 50.0 ohm No If less than (Also an dbNode and bNode 1.0e−3ohm, instance reset to parameter) 1.0e−3ohm RBSB Resistance connected between 50.0 ohm No If less than (Also an sbNode and bNode 1.0e−3ohm, instance reset to parameter) 1.0e−3ohm GBMIN Conductance in parallel with each of 1.0e−12mho No Warning the five substrate resistances to avoid message potential numerical instability due to issued if unreasonably too large a substrate less than resistance 1.0e−20 mho A.10 Flicker and Thermal Noise Model Parameters NOIA Flicker noise parameter A 6.25e41 No — (eV)⁻¹s^(1−EF)m⁻³ for NMOS; 6.188e40 (eV)⁻¹s^(1−EF)m⁻³ for PMOS NOIB Flicker noise parameter B 3.125e26 No — (eV)⁻¹s^(1−EF)m⁻¹ for NMOS; 1.5e25 (eV)⁻¹s^(1−EF)m⁻¹ for PMOS NOIC Flicker noise parameter C 8.75 No — (eV)⁻¹s^(1−EF)m EM Saturation field 4.1e7V/m No — AF Flicker noise exponent 1.0 No — EF Flicker noise frequency exponent 1.0 No — KY Flicker noise coefficient 0.0 No — A^(2−EF)s^(1−EF)F NTNOI Noise factor for short-channel devices 1.0 No − for TNOIMOD = 0 only TNOIA Coefficient of channel-length depen- 1.5 No — dence of total channel thermal noise TNOIB Channel-length dependence parameter 3.5 No — for channel thermal noise partitioning A.11 Layout-Dependent Parasitics Model Parameters DMCG Distance from S/D contact center to 0.0 m No — the gate edge DMCI Distance from S/D contact center to DMCG No — the isolation edge in the channel- length direction DMDG Same as DMCG but for merged 0.0 m No — device only DMCGT DMCG of test structures 0.0 m No — NF Number of device fingers 1 No Fatal error (instance if less than parameter one only) DWJ Offset of the S/D junction width DWC (in No — CVmodel) MIN Whether to minimize the number of 0 No — (instance drain or source diffusions for even- (minimize parameter number fingered device the drain dif- only) fusion number) XGW Distance from the gate contact to the 0.0 m No — channel edge XGL Offset of the gate length due to varia- 0.0 m No — tions in patterning XL Channel length offset due to mask/ 0.0 m No — etch effect XW Channel width offset due to mask/etch 0.0 m No — effect NGCON Number of gate contacts 1 No Fatal error if less than one; if not equal to I or 2, warn- ing mes- sage issued and reset to 1 A.12 Asymmetric Source/Drain Junction Diode Model Parameters (separate for source and drain side as indicated in the names) IJTHSREV Limiting current in reverse bias region IJTHSREV = No If not posi- IJTHDREV 0.1 A tive, reset IJTHDREV = to 0.1 A IJTHSREV IJTHSFWD Limiting current in forward bias IJTHSFWD = No If not posi- IJTHDFWD region 0.1 A tive, reset IJTHDFWD = IJTHSFWD XJBVS Fitting parameter for diode break- XJBVS = 1.0 No Note-8 XJBVD down XJBVD = XJBVS BVS Breakdown voltage BVS = 10.0 V No If not posi BVD BVD = BVS tive, reset to 10.0 V JSS Bottom junction reverse saturation JSS = No — JSD current density 1.0e−4 A/m² JSD = JSS JSWS Isolation-edge sidewall reverse satura- JSWS = No — JSWD tion current density 0.0 A/m JSWD = JSWS JSWGS Gate-edge sidewall reverse saturation JSWGS = No — JSWGD current density 0.0 A/m JSWGD = JSWGS CJS Bottom junction capacitance per unit CJS = 5.0e−4 No — CJD area at zero bias F/m² CJD = CJS MJS Bottom junction capacitance grating MJS = 0.5 No — MID coefficient MJD = MJS MJSWS Isolation-edge sidewall junction MJSWS = No — MJSWD capacitance grading coefficient 0.33 MJSWD = MJSWS CJSWS Isolation-edge sidewall junction CJSWS = No — CJSWD capacitance per unit area 5.0e−10 F/m CJSWD = CJSWS CJSWGS Gate-edge sidewall junction capaci- CJSWGS = No — CJSWGD tance per unit length CJSWS CJSWGD = CJSWS MISWGS Gate-edge sidewall junction capaci- MJSWGS = No — MJSWGD tance grading coefficient MJSWS MJSWGD = MJSWS PB Bottom junction bnilt-in potential PBS = 1.0 V No — PBD = PBS PBSWS Isolation-edge sidewall junction built- PBSWS = No — PBSWD in potential 1.0 V PBSWD = PBSWS PBSWGS Gate-edge sidewall junction built-in PBSWGS = No — PBSWGD potential PBSWS PBSWGD = PBSWS A.13 Temperature Dependence Parameters TNOM Temperature at which parameters are 27° C. No — extracted UTE Mobility temperature exponent −1.5 Yes — KT1 Temperature coefficient for threshold −0.11 V Yes — voltage KT1L Channel length dependence of the 0.0 Vm Yes — temperature coefficient for threshold voltage KT2 Body-bias coefficient of Vth tempera- 0.022 Yes — ture effect UA1 Temperature coefficient for UA 1.0e−9m/V Yes — UBI Temperature coefficient for UB −1.Oe−18 Yes — (m/V)² UC1 Temperature coefficient for UC 0.067 V⁻¹ for Yes — MOBMOD = 1; 0.025 m/V² for MOBMOD = 0 and 2 AT Temperature coefficient for satura- 3.3e4m/s Yes — tion velocity PRT Temperature coefficient for Rdsw 0.0 ohm-m Yes — NIS, NJD Emission coefficients of junction for NJS = 1.0; No — source and drain junctions, respec- NJD = NJS tively XTIS, XTID Junction current temperature expo- XTIS = 3.0; No — nents for source and drain junctions, XTID = XTIS respectively TPB Temperature coefficient of PB 0.0 V/K No — TPBSW Temperature coefficient of PBSW 0.0 V/K No — TPBSWG Temperature coefficient of PBSWG 0.0 V/K No — TCJ Temperature coefficient of CJ 0.0 K⁻¹ No — TCJSW Temperature coefficient of CJSW 0.0 K⁻¹ No — TCJSWG Temperature coefficient of CJSWG 0.0 K⁻¹ No — A.14 dW and dL Parameters WL Coefficient of length dependence for 0.0 m^(WLN) No — width offset WLN Power of length dependence of width 1.0 No — offset WW Coefficient of width dependence for 0.0 m^(WWN) No — width offset WWN Power of width dependence of width 1.0 No — offset WWL Coefficient of length and width cross 0.0 No — term dependence for width offset m^(WWN+WLN) LL Coefficient of length dependence for 0.0 m^(LLN) No — length offset LLN Power of length dependence for 1.0 No — length offset LW Coefficient of width dependence for 0.0 m^(LWN) No — length offset LWN Power of width dependence for length 1.0 No — offset LWL Coefficient of length and width cross 0.0 No — term dependence for length offset m^(LWN+LLN) LLC Coefficient of length dependence for LL No — CV channel length offset LWC Coefficient of width dependence for LW No — CV channel length offset LWLC Coefficient of length and width cross- LWL No — term dependence for CV channel length offset WLC Coefficient of length dependence for WL No — CV channel width offset WWC Coefficient of width dependence for WW No — CV channel width offset WWLC Coefficient of length and width cross- WWL No — term dependence for CV channel width offset NOTES: Note-1: If γ₁ is not given, it is calculated by $\gamma_{1} = \frac{\sqrt{2q\quad ɛ_{si}{NDEP}}}{C_{oxe}}$ If γ₂ is not given, it is calculated by $\gamma_{2} = \frac{\sqrt{2q\quad ɛ_{si}{NSUB}}}{C_{oxe}}$ Note-2: If NDEP is not given and γ₁ is given, NDEP is calculated from ${NDEP} = \frac{\gamma_{1}^{2}C_{oxe}^{2}}{2q\quad ɛ_{si}}$ If both γ₁ and NDEP are not given, NDEP defaults to 1.7e17 cm⁻³ and γ₁ is calculated from NDEP. Note-3: If VBX is not given, it is calculated by $\frac{{qNDEP} \cdot {XT}^{2}}{2ɛ_{si}} = {\Phi_{s} - {VBX}}$ Note-4: If VTH0 is not given, it is calculated by ${VTH0} = {{VFB} + \Phi_{s} + {{K1}\sqrt{\Phi_{s} - V_{bs}}}}$ where VFB = −1.0. If VTH0 is given, VFB defaults to ${VFB} = {{VTH0} - \Phi_{s} - {{K1}\sqrt{\Phi_{s} - V_{bs}}}}$ Note-5: If K₁ and K₂ are not given, they are calculated by $\begin{matrix} {{K1} = {\gamma_{2} - {2{K2}\sqrt{\Phi_{s} - {VBM}}}}} \\ {{K2} = \frac{\left( {\gamma_{1} - \gamma_{2}} \right)\left( {\sqrt{\Phi_{s} - {VBX}} - \sqrt{\Phi_{s}}} \right)}{{2\sqrt{\Phi_{s}}\left( {\sqrt{\Phi_{s} - {VBM}} - \sqrt{\Phi_{s}}} \right)} + {VBM}}} \end{matrix}\quad$ Note-6: If CGSO is not given, it is calculated by If(DLC is given and > 0.0) CGSO = DLC · C_(oxe) − CGSL if (CGSO < 0.0), CGSO = 0.0 Else CGSO = 0.6 · XJ · C_(oxe) If CGDO is not given, it is calculated by If(DLC is given and > 0.0) CGDO = DLC · C_(oxe) − CGDL if(CGDO < 0.0), CGDO = 0.0 Else CGDO = 0.6 · XJ · C_(oxe) If CGBO is not given, it is calculated by CGBO = 2 · DWC · C_(oxe) Note-7: If CF is not given, it is calculated by ${CF} = {\frac{2 \cdot {EPSROX} \cdot ɛ_{0}}{\pi} \cdot {\log\left( {1 + \frac{{4.0e} - 7}{TOXE}} \right)}}$ Note-8: For dioMod = 0, if XJBVS < 0.0, it is reset to 1.0. For dioMod = 2, if XJBVS <= 0.0, it is reset to 1.0. For dioMod = 0, if XJBVD < 0.0, it is reset to 1.0. For dioMod = 2, if XJBVD <= 0.0, it is reset to 1.0. Poly Silicon Gate Depletion $\begin{matrix} {V_{poly} = {{0.5X_{poly}E_{poly}} = \frac{{qNGATE} \cdot X_{poly}^{2}}{2\quad ɛ_{si}}}} & \left( {1.2{.1}} \right) \\ {{{EPSROX} \cdot E_{ox}} = {{ɛ_{si}E_{poly}} = \sqrt{2\quad q\quad ɛ_{si}{{NGATE} \cdot V_{poly}}}}} & \left( {1.2{.2}} \right) \\ {{V_{gs} - V_{FB} - \Phi_{s}} = {V_{poly} + V_{ox}}} & \left( {1.2{.3}} \right) \\ {{{a\left( {V_{gs} - V_{FB} - \Phi_{s} - V_{poly}} \right)}^{2} - V_{poly}} = 0} & \left( {1.2{.4}} \right) \end{matrix}$  V _(gs) −V _(FB)−Φ_(s) =V _(poly) V _(ox)  (1.2.3) a(V _(gs) −V _(FB)−Φ_(s) −V _(poly))² V _(poly)=0  (1.2.4) where $\begin{matrix} {a = \frac{{EPSROX}^{2}}{2q\quad ɛ_{si}{{NGATE} \cdot {TOXE}^{2}}}} & \left( {1.2{.5}} \right) \\ {V_{gse} = {{VFB} + \Phi_{s} + \frac{q\quad ɛ_{si}{{NGATE} \cdot {TOXE}^{2}}}{{EPSROX}^{2}}}} & \left( {1.2{.6}} \right) \\ {\quad\left( {\sqrt{1 + \frac{2{{EPSROX}^{2}\left( {V_{gs} - {VFB} - \Phi_{s}} \right)}}{q\quad ɛ_{si}{{NGATE} \cdot {TOXE}^{2}}}} - 1} \right)} & \quad \end{matrix}$ Effective Channel Length and Width $\begin{matrix} {L_{eff} = {L_{drawn} + {XL} - {2d\quad L}}} & \left( {1.3{.1}} \right) \\ {W_{eff} = {\frac{W_{drawn}}{NF} + {XW} - {2{dW}}}} & \left( {1.3{.2}a} \right) \\ {W_{eff}^{\prime} = {\frac{W_{drawn}}{NF} + {XW} - {2{dW}^{\prime}}}} & \left( {1.3{.2}b} \right) \\ {{dW} = {{dW}^{\prime} + {{DWG} \cdot V_{gsteff}} + {{DWB}\left( {\sqrt{\Phi_{s} - V_{bseff}} - \sqrt{\Phi_{s}}} \right)}}} & \left( {1.3{.3}} \right) \\ {{dW}^{\prime} = {{WINT} + \frac{WL}{L^{WLN}} + \frac{WW}{W^{WWN}} + \frac{WWL}{L^{WLN}W^{WWN}}}} & \quad \\ {{dL} = {{LINT} + \frac{LL}{L^{LLN}} + \frac{LW}{W^{LWN}} + \frac{LWL}{L^{LLN}W^{LWN}}}} & \left( {1.3{.4}} \right) \\ {L_{active} = {L_{drawn} + {XL} - {2{dL}}}} & \left( {1.3{.5}} \right) \\ {W_{active} = {\frac{W_{drawn}}{NF} + {XW} - {2{dW}}}} & \left( {1.3{.6}} \right) \\ {{dL} = {{DLC} + \frac{LLC}{L^{LLN}} + \frac{LWC}{W^{LWN}} + \frac{LWLC}{L^{LLN}W^{LWN}}}} & \left( {1.3{.7}} \right) \\ {{dW} = {{DWC} + \frac{WLC}{L^{WLN}} + \frac{WWC}{W^{WWN}} + \frac{WWLC}{L^{WLN}W^{WWN}}}} & \left( {1.3{.8}} \right) \\ {W_{effcj} = {\frac{W_{drawn}}{NF} -}} & \left( {1.3{.9}} \right) \\ {\quad{2 \cdot \left( {{DWJ} + \frac{WLC}{L^{WLN}} + \frac{WWC}{W^{WWN}} + \frac{WWLC}{L^{WLN}W^{WWN}}} \right)}} & \quad \end{matrix}$ Long Channel Model with Uniform Doping $\begin{matrix} {V_{th} = {{VFB} + \Phi_{s} + {\gamma\sqrt{\Phi_{s} - V_{bs}}}}} & \left( {2.1{.1}} \right) \\ {\quad{= {{VTH0} + {\gamma\left( {\sqrt{\Phi_{s} - V_{bs}} - \sqrt{\Phi_{s}}} \right)}}}} & \quad \\ {\gamma = \frac{\sqrt{2q\quad ɛ_{si}N_{substrate}}}{C_{oxe}}} & \left( {2.1{.2}} \right) \end{matrix}$ Long Channel Model with Non-Uniform Doping $\begin{matrix} \begin{matrix} {V_{th} = {V_{{th},{NDEP}} + \frac{{qD}_{0}}{C_{oxe}} +}} \\ {{K1}_{NDEP}\left( {\sqrt{\varphi_{s} - V_{bs} - \frac{{qD}_{1}}{ɛ_{si}}} - \sqrt{\varphi_{s} - V_{bs}}} \right)} \end{matrix} & \left( {2.2{.1}} \right) \end{matrix}$

-   -   where K1_(NDEP) is the body-bias coefficient for         N_(substrate)=NDEP,         V _(th,NDEP) =VTH0+K1_(NDEP)({square root}{square root over         (φ_(s) −V _(bs))}−{square root}{square root over         (φ_(s))})  (2.2.2)         with a definition of $\begin{matrix}         {\psi_{s} = {0.4 + {\frac{k_{B}T}{q}{\ln\left( \frac{NDEP}{n_{i}} \right)}}}} & \left( {2.2{.3}} \right) \\         {D_{0} = {{D_{00} + D_{01}} = {{\int_{0}^{X_{dep}0}{\left( {{N(x)} - {NDEP}} \right)\quad{\mathbb{d}x}}} + {\int_{X_{dep}0}^{X_{dep}}{\left( {{N(x)} - {NDEP}} \right)\quad{\mathbb{d}x}}}}}} & \left( {2.2{.4}} \right) \\         {D_{1} = {{D_{10} + D_{11}} = {{\int_{0}^{X_{dep}0}{\left( {{N(x)} - {NDEP}} \right)x\quad{\mathbb{d}x}}} + {\int_{x_{dep}0}^{X_{dep}}{\left( {{N(x)} - {NDEP}} \right)x\quad{\mathbb{d}x}}}}}} & \left( {2.2{.5}} \right) \\         {V_{th} = {{{VTH}\quad 0} + {K\quad 1\left( {\sqrt{\Phi_{s} - V_{bs}} - \sqrt{\Phi_{s}}} \right)} - {K\quad{2 \cdot V_{bs}}}}} & \left( {2.2{.6}} \right)         \end{matrix}$  V _(th) =VTH0+K1({square root}{square root over         (Φ_(s) −V _(bs))}−{square root}{square root over (Φ_(s))})−K2·V         _(bs)  (2.2.6)         where K2=qC₀₁/C_(oxe), and the surface potential is defined as         $\begin{matrix}         {\Phi_{s} = {0.4 + {\frac{k_{B}T}{q}{\ln\left( \frac{NDEP}{n_{i}} \right)}} + {PHIN}}} & \left( {2.2{.7}} \right)         \end{matrix}$         where         PHIN=−qD ₁₀/ε_(si)         K1=γ₂−2K2{square root}{square root over (Φ_(s) −VBM)}  (2.2.8)         $\begin{matrix}         {{PHIN} = {{- {qD}_{10}}/ɛ_{si}}} & \quad \\         {{K1} = {\gamma_{2} - {2{K2}\sqrt{\Phi_{s} - {VBM}}}}} & \left( {2.2{.8}} \right) \\         {{K2} = \frac{\left( {\gamma_{1} - \gamma_{2}} \right)\left( {\sqrt{\Phi_{s} - {VBX}} - \sqrt{\Phi_{s}}} \right)}{{2\sqrt{\Phi_{s}}\left( {\sqrt{\Phi_{s} - {VBM}} - \sqrt{\Phi_{s}}} \right)} + {VBM}}} & \left( {2.2{.9}} \right) \\         {\gamma_{1} = \frac{\sqrt{2q\quad ɛ_{si}{NDEP}}}{C_{oxe}\quad}} & \left( {2.2{.10}} \right) \\         {\gamma_{2} = \frac{\sqrt{2q\quad ɛ_{si}{NSUB}}}{C_{oxe}}} & \left( {2.2{.11}} \right) \\         {\frac{{qNDEP} \cdot {XT}^{2}}{2ɛ_{si}} = {\Phi_{s} - {VBX}}} & \left( {2.2{.12}} \right)         \end{matrix}$         Non-Uniform Lateral Doping $\begin{matrix}         \begin{matrix}         {V_{th} = {{VTH0} + {{{K1}\left( {\sqrt{\Phi_{s} - V_{bs}} - \sqrt{\Phi_{s}}} \right)} \cdot \sqrt{1 + \frac{LPEB}{L_{eff}}}} -}} \\         {{{K2} \cdot V_{bs}} + {{{K1}\left( {\sqrt{1 + \frac{LPE0}{L_{eff}}} - 1} \right)}\sqrt{\Phi_{s}}}}         \end{matrix} & \left( {2.3{.1}} \right) \\         {{\Delta\quad{V_{th}({DITS})}} = {{- {nv}_{t}} \cdot {\ln\left( \frac{\left( {1 - {\mathbb{e}}^{{- V_{ds}}/v_{t}}} \right) \cdot L_{eff}}{L_{eff} + {{DVTP0} \cdot \left( {1 + {\mathbb{e}}^{{- {DVTP1}} \cdot V_{ds}}} \right)}} \right)}}} & \left( {2.3{.2}} \right) \\         {{\Delta\quad{V_{th}({DITS})}} = {{- {nv}_{t}} \cdot {\ln\left( \frac{L_{eff}}{L_{eff} + {{DVTP0} \cdot \left( {1 + {\mathbb{e}}^{{- {DVTP1}} \cdot V_{ds}}} \right)}} \right)}}} & \left( {2.3{.3}} \right)         \end{matrix}$         Short-Channel and DIBL Effect         ΔV _(th)(SCE,DIBL)=−θ_(th)(L _(eff))·[2(V _(bi)−Φ_(s))+V         _(ds)]  (2.4.1) $\begin{matrix}         {{\Delta\quad{V_{th}\left( {{SCE},{DIBL}} \right)}} = {{- {\theta_{th}\left( L_{eff} \right)}} \cdot \left\lbrack {{2\left( {V_{bi} - \Phi_{s}} \right)} + V_{ds}} \right\rbrack}} & \left( {2.4{.1}} \right) \\         {V_{bi} = {\frac{k_{B}T}{q}{\ln\left( \frac{{NDEP} \cdot {NSD}}{n_{i}^{2}} \right)}}} & \left( {2.4{.2}} \right) \\         {{\theta_{th}\left( L_{eff} \right)} = \frac{0.5}{{\cosh\left( \frac{L_{eff}}{l_{t}} \right)} - 1}} & \left( {2.4{.3}} \right) \\         {l_{t} = \sqrt{\frac{ɛ_{si} \cdot {TOXE} \cdot X_{dep}}{{EPSROX} \cdot \eta}}} & \left( {2.4{.4}} \right) \\         {X_{dep} = \sqrt{\frac{2{ɛ_{si}\left( {\Phi_{s} - V_{bs}} \right)}}{qNDEP}}} & \left( {2.4{.5}} \right) \\         {{\theta_{th}\left( L_{eff} \right)} = {{\exp\left( {- \frac{L_{eff}}{2l_{t}}} \right)} + {2{\exp\left( {- \frac{L_{eff}}{l_{t}}} \right)}}}} & \left( {2.4{.6}} \right) \\         {{\theta_{th}({SCE})} = \frac{0.5 \cdot {DVT0}}{{\cosh\left( {{DVT1} \cdot \frac{L_{eff}}{l_{t}}} \right)} - 1}} & \left( {2.4{.7}} \right) \\         {{\Delta\quad{V_{th}({SCE})}} = {{- {\theta_{th}({SCE})}} \cdot \left( {V_{bi} - \Phi_{s}} \right)}} & \left( {2.4{.8}} \right) \\         {l_{t} = {\sqrt{\frac{ɛ_{si} \cdot {TOXE} \cdot X_{dep}}{EPSROX}} \cdot \left( {1 + {{DVT2} \cdot V_{bs}}} \right)}} & \left( {2.4{.9}} \right) \\         {{\theta_{th}({DIBL})} = \frac{0.5}{{\cosh\left( {{DSUB} \cdot \frac{L_{eff}}{l_{t0}}} \right)} - 1}} & \left( {2.4{.10}} \right) \\         {{{\Delta V}_{th}({DIBL})} = {{- {\theta_{th}({DIBL})}} \cdot \left( {{ETA0} + {{ETAB} \cdot V_{bs}}} \right) \cdot V_{ds}}} & \left( {2.4{.11}} \right) \\         {l_{t0} = \sqrt{\frac{ɛ_{si} \cdot {TOXE} \cdot X_{dep0}}{EPSROX}}} & \left( {2.4{.12}} \right) \\         {X_{dep0} = \sqrt{\frac{2ɛ_{si}\Phi_{s}}{qNDEP}}} & \left( {2.4{.13}} \right)         \end{matrix}$         Narrow Width Effect $\begin{matrix}         {\frac{\pi\quad{{qNDEP} \cdot X_{{dep},\max}^{2}}}{2C_{axe}W_{eff}} = {3\pi\frac{TOXE}{W_{eff}}\Phi_{s}}} & \left( {2.5{.1}} \right) \\         {{\Delta\quad{V_{th}({Narrow\_ width1})}} = {\left( {{K3} + {{K3B} \cdot V_{bs}}} \right)\frac{TOXE}{W_{eff}^{\prime} + {W0}}\Phi_{s}}} & \left( {2.5{.2}} \right) \\         {{\Delta\quad{V_{th}({Narrow\_ width2})}} = {{- \frac{0.5 \cdot {DVT0W}}{{\cosh\left( {{DVT1W} \cdot \frac{L_{eff}W_{eff}^{\prime}}{l_{tw}}} \right)} - 1}} \cdot \quad\left( {V_{bi} - \Phi_{s}} \right)}} & \left( {2.5{.3}} \right) \\         {l_{tw} = {\sqrt{\frac{ɛ_{si} \cdot {TOXE} \cdot X_{dep}}{EPSROX}} \cdot \left( {1 + {{DVT2W} \cdot V_{bs}}} \right)}} & \left( {2.5{.4}} \right) \\         \begin{matrix}         {V_{th} = {{VTH0} +}} \\         {{\left( {{K_{1{ox}} \cdot \sqrt{\Phi_{s} - V_{bseff}}} - {{K1} \cdot \sqrt{\Phi_{s}}}} \right)\sqrt{1 + \frac{LPEB}{L_{eff}}}} -} \\         {{K_{2{ox}}V_{bseff}} + {{K_{1{ox}}\left( {\sqrt{1 + \frac{LPE0}{L_{eff}}} - 1} \right)}\sqrt{\Phi_{s}}} +} \\         {{\left( {{K3} + {{K3B} \cdot V_{bseff}}} \right)\frac{TOXE}{W_{eff}^{\prime} + {W0}}\Phi_{s}} - {0.5 \cdot}} \\         {\left\lbrack {\frac{DVT0W}{{\cosh\left( {{DVT1W}\quad\frac{L_{eff}W_{eff}^{\prime}}{l_{tw}}} \right)} - 1} +} \right.} \\         {{\left. \frac{DVT0}{{\cosh\left( {{DVT1}\quad\frac{L_{eff}}{l_{t}}} \right)} - 1} \right\rbrack\left( {V_{bi} - \Phi_{s}} \right)} -} \\         {\frac{0.5}{{\cosh\left( {{DSUB}\quad\frac{L_{eff}}{l_{t0}}} \right)} - 1}{\left( {{ETA0} + {{ETAB} \cdot V_{bseff}}} \right) \cdot V_{ds}}}         \end{matrix} & \left( {2.5{.5}} \right) \\         {K_{1{ox}} = {{K1} \cdot \frac{TOXE}{TOXM}}} & \left( {2.5{.6}} \right) \\         {and} & \quad \\         {K_{2{ox}} = {{K2} \cdot \frac{TOXE}{TOXM}}} & \left( {2.5{.7}} \right) \\         {V_{bseff} = {V_{bc} + {0.5 \cdot \left\lbrack {\left( {V_{bs} - V_{bc} - \delta_{1}} \right) + \quad\sqrt{\left( {V_{bs} - V_{bc} - \delta_{1}} \right)^{2} - {4{\delta_{1} \cdot V_{bc}}}}} \right\rbrack}}} & \left( {2.5{.8}} \right) \\         {V_{bc} = {0.9\left( {\Phi_{s} - \frac{{K1}^{2}}{4{K2}^{2}}} \right)}} & \left( {2.5{.9}} \right)         \end{matrix}$         Channel Charge Model $\begin{matrix}         {Q_{chsubs0} = {\sqrt{\frac{{qNDEPɛ}_{si}}{2\Phi_{s}}}{v_{t} \cdot {\exp\left( \frac{V_{gse} - V_{th} - {Voff}^{\prime}}{{nv}_{t}} \right)}}}} & \left( {3.1{.1}} \right)         \end{matrix}$         where $\begin{matrix}         {{Voff}^{\prime} = {{VOFF} + \frac{VOFFL}{L_{eff}}}} & \left( {3.1{.1}a} \right) \\         {Q_{chs0} = {C_{oxe} \cdot \left( {V_{gse} - V_{th}} \right)}} & \left( {3.1{.2}} \right) \\         {Q_{ch0} = {C_{oxeff} \cdot V_{gsteff}}} & \left( {3.1{.3}} \right) \\         {C_{oxeff} = {{\frac{C_{oxe} \cdot C_{cen}}{C_{axe} + C_{cen}}\quad{with}\quad C_{cen}} = \frac{ɛ_{xi}}{X_{DC}}}} & \left( {3.1{.4}} \right) \\         {X_{DC} = \frac{1.9 \times 10^{- 9}{cm}}{1 + \left( \frac{V_{gsteff} + {4\left( {{VTH0} - {VFB} - \Phi_{s}} \right)}}{2{TOXP}} \right)^{0.7}}} & \left( {3.1{.5}} \right) \\         {V_{gsteff} = \frac{{nv}_{t}\ln\left\{ {1 + {\exp\left\lbrack \frac{m^{*}\left( {V_{gse} - V_{th}} \right)}{{nv}_{t}} \right\rbrack}} \right\}}{m^{*} + {{{nC}_{oxe} \cdot \sqrt{\frac{2\Phi_{s}}{{qNDEP}\quad ɛ_{si}}}}{\exp\left\lbrack {- \frac{{\left( {1 - m^{*}} \right)\left( {V_{gse} - V_{th}} \right)} - {Voff}^{\prime}}{{nv}_{t}}} \right\rbrack}}}} & \left( {3.1{.6}a} \right)         \end{matrix}$         where $\begin{matrix}         {{m\text{*}} = {0.5 + \frac{\arctan({MINV})}{\pi}}} & \left( {3.1{.6}b} \right) \\         {{Q_{chs}(y)} = {C_{axeff} \cdot \left( {V_{gse} - V_{th} - {A_{bulk}{V_{F}(y)}}} \right)}} & \left( {3.1{.7}} \right) \\         {{Q_{chs}(y)} = {Q_{chr0} + {{\Delta Q}_{chs}(y)}}} & \left( {3.1{.8}} \right) \\         {{Q_{chsubs}(y)} = {Q_{chsubs0} \cdot {\exp\left( {- \frac{A_{bulk}{V_{F}(y)}}{{nv}_{i}}} \right)}}} & \left( {3.1{.9}} \right) \\         {{Q_{{chsubs}\quad}(y)} = {Q_{chsubs0}\left( {1 - \frac{A_{bulk}{V_{F}(y)}}{{nv}_{i}}} \right)}} & \left( {3.1{.10}} \right) \\         {{Q_{chsubs}(y)} = {Q_{chsubs0} + {{\Delta Q}_{chsubs}(y)}}} & \left( {3.1{.11}} \right) \\         {{{\Delta Q}_{chsubs}(y)} = {{- Q_{chsubs0}} \cdot \frac{A_{bulk}{V_{F}(y)}}{{nv}_{i}}}} & \left( {3.1{.12}} \right) \\         {{{\Delta Q}_{ch}(y)} = \frac{{{\Delta Q}_{chs}(y)} \cdot {{\Delta Q}_{chsubs}(y)}}{{{\Delta Q}_{chs}(y)} + {{\Delta Q}_{chsubs}(y)}}} & \left( {3.1{.13}} \right) \\         {{{\Delta Q}_{ch}(y)} = {{- \frac{V_{F}(y)}{V_{b}}}Q_{ch0}}} & \left( {3.1{.14}} \right) \\         {V_{b} = \frac{V_{gtseff}2\nu\quad t}{A_{bulk}}} & \left( {3.1{.15}} \right) \\         {{Q_{ch}(y)} = {C_{axeff} \cdot V_{gsteff} \cdot \left( {1 - \frac{V_{F}(y)}{V_{b}}} \right)}} & \left( {3.1{.16}} \right)         \end{matrix}$         Subthreshold Swing $\begin{matrix}         {I_{ds} = {{I_{0}\left\lbrack {1 - {\exp\left( {- \frac{V_{ds}}{v_{t}}} \right)}} \right\rbrack} \cdot {\exp\left( \frac{V_{gs} - V_{th} - V_{off}^{\prime}}{{nv}_{t}} \right)}}} & \left( {3.2{.1}} \right)         \end{matrix}$         where $\begin{matrix}         {I_{0} = {\mu\frac{W}{L}\sqrt{\frac{q\quad ɛ_{si}{NDEP}}{2\Phi_{s}}v_{t}^{2}}}} & \left( {3.2{.2}} \right) \\         {{n = {1 + {{NFACTOR} \cdot \frac{C_{dep}}{C_{oxe}}} + \frac{{Cdsc\_ Term} + {CIT}}{C_{oxe}}}}{{Cdsc\_ Term} = {\left( {{CDSC} + {{CDSCD} \cdot V_{ds}} + {{CDSCB} \cdot V_{bseff}}} \right) \cdot \frac{0.5}{{\cosh\left( {{DVT1}\frac{L_{eff}}{l_{t}}} \right)} - 1}}}} & \left( {3.2{.3}} \right)         \end{matrix}$         Voltage Across Oxide $\begin{matrix}         {V_{oxacc} = {V_{fbzb} - V_{FBeff}}} & \left( {4.2{.1}a} \right) \\         {V_{oxdepinv} = {{K_{lox}\sqrt{\Phi_{s}}} + V_{gsteff}}} & \left( {4.2{.1}b} \right) \\         {V_{fbzb} = \left. V_{th} \middle| {}_{{zeroV}_{bs}\quad{and}\quad v_{ds}}{{- \Phi_{s}} - {K\quad 1\sqrt{\Phi_{s}}\quad\text{and}}} \right.} & \left( {4.2{.2}} \right) \\         {V_{FBeff} = {V_{fbzb} - {0.5\left\lbrack {\left( {V_{fbzb} - V_{gb} - 0.02} \right) + \sqrt{\left( {V_{fbzb} - V_{gb} - 0.02} \right)^{2} + {0.08V_{fbzb}}}} \right\rbrack}}} & \left( {4.2{.3}} \right)         \end{matrix}$         Gate to Substrate Current $\begin{matrix}         {{{Igbacc} = {W_{eff}{L_{eff} \cdot A \cdot T_{oxRatio} \cdot V_{gb} \cdot V_{aux} \cdot {\exp\left\lbrack {{- B} \cdot {{TOXE}\left( {{AIGBACC} - {{BIGBACC} \cdot V_{oxacc}}} \right)} \cdot \left( {1 + {{CIGBACC} \cdot V_{oxacc}}} \right)} \right\rbrack}}}}{T_{oxRatio} = {\left( \frac{TOXREF}{TOXE} \right)^{NTOX} \cdot \frac{1}{{TOXE}^{2}}}}{V_{aux} = {{NIGBACC} \cdot v_{t} \cdot {\log\left( {1 + {\exp\left( {- \frac{V_{gb} - V_{fbzb}}{{NIGBACC} \cdot v_{t}}} \right)}} \right)}}}} & \left( {4.3{.1}} \right) \\         {{{Igbinv} = {W_{eff}{L_{eff} \cdot A \cdot T_{oxRatio} \cdot V_{gb} \cdot V_{aux} \cdot {\exp\left\lbrack {{- B} \cdot {{TOXE}\left( {{AIGBINV} - {{BIGBINV} \cdot V_{oxdepinv}}} \right)} \cdot \left( {1 + {{CIGBINV} \cdot V_{oxdepinv}}} \right)} \right\rbrack}}}}{V_{aux} = {{NIGBINV} \cdot v_{t} \cdot {\log\left( {1 + {\exp\left( \frac{V_{oxdepinv} - {EIGBINV}}{{EIGBINV} \cdot v_{t}} \right)}} \right)}}}} & \left( {4.3{.2}} \right)         \end{matrix}$         Gate to Channel Current $\begin{matrix}         {{{Igc} = {W_{eff}{L_{eff} \cdot A \cdot T_{oxRatio} \cdot V_{gse} \cdot V_{aux} \cdot {\exp\left\lbrack {{- B} \cdot {{TOXE}\left( {{AIGC} - {{BIGC} \cdot V_{oxdepinv}}} \right)} \cdot \left( {1 + {{CIGC} \cdot V_{oxdepinv}}} \right)} \right\rbrack}}}}{V_{aux} = {{NIGC} \cdot v_{t} \cdot {\log\left( {1 + {\exp\left( \frac{V_{gse} - {VTH0}}{{NIGC} \cdot v_{t}} \right)}} \right)}}}} & \left( {4.3{.3}} \right) \\         {{{Igs} = {W_{eff}{{DLCIG} \cdot A \cdot T_{oxRatioEdge} \cdot V_{gs} \cdot V_{gs}^{\prime} \cdot {\exp\left\lbrack {{- B} \cdot {TOXE} \cdot {POXEDGE} \cdot \left( {{AIGSD} - {{BIGSD} \cdot V_{gs}^{\prime}}} \right) \cdot \left( {1 + {{CIGSD} \cdot V_{gs}^{\prime}}} \right)} \right\rbrack}}}}{and}} & \left( {4.3{.4}} \right) \\         {{{Igd} = {W_{eff}{{DLCIG} \cdot A \cdot T_{oxRatioEdge} \cdot V_{gd} \cdot V_{gd}^{\prime} \cdot {\exp\left\lbrack {{- B} \cdot {TOXE} \cdot {POXEDGE} \cdot \left( {{AIGSD} - {{BIGSD} \cdot V_{gd}^{\prime}}} \right) \cdot \left( {1 + {{CIGSD} \cdot V_{gd}^{\prime}}} \right)} \right\rbrack}}}}{T_{oxRatioEdge} = {\left( \frac{TOXREF}{{TOXE} \cdot {POXEDGE}} \right)^{NTOX} \cdot \frac{1}{\left( {{TOXE} \cdot {POXEDGE}} \right)^{2}}}}{V_{gs}^{\prime} = \sqrt{\left( {V_{gs} - V_{fbsd}} \right)^{2} + {1.0e} - 4}}{V_{gd}^{\prime} = \sqrt{\left( {V_{gd} - V_{fbsd}} \right)^{2} + {1.0e} - 4}}{V_{fbsd} = {\frac{k_{B}T}{q}{\log\left( \frac{NGATE}{NSD} \right)}}}} & \left( {4.3{.5}} \right)         \end{matrix}$         Partition         Igc=Igcs+Igcd $\begin{matrix}         {{{Igc} = {{Igcs} + {Igcd}}}{{Igcs} = {{Igc} \cdot \frac{{{PIGCD} \cdot V_{ds}} + {\exp\left( {{- {PIGCD}} \cdot V_{ds}} \right)} - 1 + {1.0e} - 4}{{{PIGCD}^{2} \cdot V_{ds}^{2}} + {2.0e} - 4}}}} & \left( {4.3{.6}} \right) \\         {{Igcd} = {{Igc} \cdot \frac{1 - {\left( {{{PIGCD} \cdot V_{ds}} + 1} \right) \cdot {\exp\left( {{- {PIGCD}} \cdot V_{ds}} \right)}} + {1.0e} - 4}{{{PIGCD}^{2} \cdot V_{ds}^{2}} + {2.0e} - 4}}} & \left( {4.3{.7}} \right)         \end{matrix}$         Drain Current Model

Bulk Charge Effect $\begin{matrix} {A_{bulk} = {\left\{ {1 + {{F\_ doping} \cdot \begin{bmatrix} \begin{matrix} {\frac{{A0} \cdot L_{eff}}{L_{eff} + {2\sqrt{{XJ} \cdot X_{dep}}}} \cdot} \\ {\left( {1 - {{AGS} \cdot {V_{gstef}\left( \frac{L_{eff}}{L_{eff} + {2\sqrt{{XJ} \cdot X_{dep}}}} \right)}^{2}}} \right) +} \end{matrix} \\ \frac{B0}{W_{eff}^{\prime} + {B1}} \end{bmatrix} \cdot}} \right\}\frac{1}{1 + {{KETA} \cdot V_{bseff}}}}} & \left( {5.1{.1}} \right) \\ {{F\_ doping} = {\frac{\sqrt{1 + {{LPEB}/L_{eff}}}K_{1{ox}}}{2\sqrt{\Phi_{s} - V_{bseff}}} + K_{2{ox}} - {{K3B}\frac{TOXE}{W_{eff}^{\prime} + {W0}}\Phi_{s}}}} & \left( {5.1{.2}} \right) \end{matrix}$

Unified Mobility Model $\begin{matrix} {E_{eff} = \frac{Q_{B} + \left( {Q_{n}/2} \right)}{ɛ_{si}}} & \left( {5.2{.1}} \right) \\ {\mu_{eff} = \frac{\mu_{0}}{1 + \left( {E_{eff}/E_{o}} \right)^{v}}} & \left( {5.2{.2}} \right) \\ {E_{eff} \approx \frac{V_{gs} + V_{ih}}{6{TOXE}}} & \left( {5.2{.3}} \right) \end{matrix}$

-   -   mobMod=0 $\begin{matrix}         {\mu_{eff} = {{\frac{U0}{1 + \left( {{UA} + {UCV}_{bseff}} \right)}\left( \frac{V_{gsteff} + {2V_{ih}}}{TOXE} \right)} + {{UB}\left( \frac{V_{gsteff} + {2V_{ih}}}{TOXE} \right)}^{2}}} & \left( {5.2{.4}} \right)         \end{matrix}$     -   mobMod=1 $\begin{matrix}         {\mu_{eff} = \frac{U0}{\begin{matrix}         {1 + \left\lbrack {{{UA}\left( \frac{V_{gsteff} + {2V_{ih}}}{TOXE} \right)} +} \right.} \\         {\left. {{UB}\left( \frac{V_{gsteff} + {2V_{ih}}}{TOXE} \right)}^{2} \right\rbrack\left( {1 + {{UC} \cdot V_{bseff}}} \right)}         \end{matrix}}} & \left( {5.2{.5}} \right)         \end{matrix}$     -   mobMod=2 $\begin{matrix}         {\mu_{eff} = \frac{U0}{\quad{1 + {\left( {{UA} + {{UC} \cdot V_{bseff}}} \right)\left\lceil \frac{V_{gsteff} + {C_{0} \cdot \left( {{VTHO} - {VFB} - {\Phi s}} \right.}}{TOXE} \right\rceil^{EU}}}\quad}} & \left( {5.2{.6}} \right)         \end{matrix}$         Asymmetric and Bias Dependent Source/Drain Resistance Model     -   rdsMod=0 $\begin{matrix}         {{R_{ds}(V)} = \quad\frac{\quad\begin{Bmatrix}         {{RDSWMIN} + {{RDSW} \cdot}} \\         \left\lbrack {{{PRWB} \cdot \left( {\sqrt{\Phi_{s} - V_{bseff}} - \sqrt{\Phi_{s}}} \right)} + \quad\frac{1}{1 + {{PRWG} \cdot V_{gseff}}}} \right\rbrack         \end{Bmatrix}}{\left( {1{{e6} \cdot W_{effcj}}} \right)^{WR}}} & \left( {5.3{.1}} \right)         \end{matrix}$     -   rdsMod=1 $\begin{matrix}         {{R_{d}(V)} = \quad\frac{\quad\begin{Bmatrix}         {{RDWMIN} + {{RDW} \cdot}} \\         {\left\lbrack {{{- {PRWB}} \cdot V_{bd}} + \quad\quad\frac{1}{1 + {{PRWG} \cdot V_{gd}} - V_{fbsd}}} \right\rbrack\quad}         \end{Bmatrix}}{\left\lbrack {\left( {1{{e6} \cdot W_{effcj}}} \right)^{WR} \cdot {NF}} \right\rbrack}} & \left( {5.3{.2}} \right) \\         {{R_{s}(V)} = \quad\frac{\quad\begin{Bmatrix}         {{RSWMIN} + {{RSW} \cdot}} \\         {\left\lbrack {{{- {PRWB}} \cdot V_{bs}} + \quad\quad\frac{1}{1 + {{PRWG} \cdot \left( {V_{gs} - V_{fbsd}} \right)}}} \right\rbrack\quad}         \end{Bmatrix}}{\left\lbrack {\left( {1{{e6} \cdot W_{effcj}}} \right)^{WR} \cdot {NF}} \right\rbrack}} & \left( {5.3{{.3}.}} \right)         \end{matrix}$         Drain Current for Triode Region     -   rdsMod=1 $\begin{matrix}         {{I_{ds}(y)} = {{{WQ}_{ch}(y)}{\mu_{ne}(y)}\frac{\mathbb{d}{V_{F}(y)}}{\mathbb{d}y}}} & \left( {5.4{.1}} \right) \\         {\mu_{{ne}{(y)}} = \frac{\mu_{eff}}{1 + \frac{E_{y}}{E_{sat}}}} & \left( {5.4{.2}} \right) \\         {{I_{ds}(y)} = {{{WQ}_{ch0}\left( {1 - \frac{V_{F}(y)}{V_{b}}} \right)}\frac{\mu_{eff}}{1 + \frac{E_{y}}{E_{sat}}}\frac{\mathbb{d}{V_{F}(y)}}{\mathbb{d}y}}} & \left( {5.4{.3}} \right) \\         {I_{ds0} = {\frac{W\quad\mu_{eff}Q_{ch0}{V_{ds}\left( {1 - \frac{V_{ds}}{2V_{b}}} \right)}}{L\left( {1 + \frac{V_{ds}}{E_{sat}L}} \right)}.}} & \left( {5.4{.4}} \right)         \end{matrix}$     -   rdsMod=0 $\begin{matrix}         {I_{ds} = \frac{I_{dso}}{1 + \frac{R_{ds}I_{dso}}{V_{ds}}}} & \left( {5.4{.5}} \right)         \end{matrix}$         Velocity Saturation $\begin{matrix}         {v = {{{\frac{\mu_{eff}E}{1 + {E/E_{sat}}}\quad E} < E_{sat}}\quad = {{{VSAT}\quad E} \geq E_{sat}}}} & \left( {5.5{.1}} \right) \\         {E_{sat} = \frac{2{VSAT}}{\mu_{eff}}} & \left( {5.5{.2}} \right)         \end{matrix}$         Saturation Voltage Vdsat

Intrinsic $\begin{matrix} {V_{dsat} = {\frac{E_{sat}{L\left( {V_{gsteff} + 2_{Vt}} \right)}}{{A_{bulk}E_{sat}L} + V_{gsteff} + 2_{vt}}.}} & \left( {5.6{.1}} \right) \end{matrix}$

Extrinsic $\begin{matrix} {V_{dsat} = \frac{{- b} - \sqrt{b^{2} - {4{ac}}}}{2a}} & \left( {5.6{.2}a} \right) \\ {a = {{A_{bulk}^{2}W_{eff}{VSATC}_{oxe}R_{ds}} + {A_{bulk}\left( {\frac{1}{\lambda} - 1} \right)}}} & \left( {5.6{.2}b} \right) \\ {b = {- \begin{bmatrix} {{\left( {V_{gsteff} + {2v_{t}}} \right)\left( {\frac{2}{\lambda} - 1} \right)} + {A_{bulk}E_{sat}L_{eff}} +} \\ {3{A_{bulk}\left( {V_{gsteff} + {2v_{t}}} \right)}W_{eff}{VSATC}_{oxe}R_{ds}} \end{bmatrix}}} & \left( {5.6{.2}c} \right) \\ {c = {{\left( {V_{gsteff} + {2v_{t}}} \right)E_{sat}L_{eff}} + {2\left( {V_{gsteff} + {2v_{t}}} \right)^{2}W_{eff}{VSATC}_{oxe}R_{ds}}}} & \left( {5.6{.2}d} \right) \\ {\lambda = {{A1V}_{gsteff} + {A2}}} & \left( {5.6{.2}e} \right) \end{matrix}$  c=(V _(gsteff)+2ν₁)E _(sat) L _(eff)+2(V _(gsteff)+2ν₁)² W _(eff) VSATC _(oxe) R _(ds)  (5.6.2d) λ=A1V _(gsteff) +A2  (5.6.2e) Vdseff $\begin{matrix} {V_{dseff} = {V_{dsat} - {\frac{1}{2}\left\lbrack {\left( {V_{dsat} - V_{ds} - \delta} \right) + \sqrt{\left( {V_{dsat} - V_{ds} - \delta^{2}} \right) + {4\quad{\delta \cdot V_{dsat}}}}} \right\rbrack}}} & \left( {5.6{.3}} \right) \end{matrix}$ Saturation-Region Output Conductance Model $\begin{matrix} {{I_{ds}\left( {V_{gs},V_{ds}} \right)} = {{I_{dsat}\left( {V_{gs},V_{dsat}} \right)} + {\int_{V_{dsat}}^{V_{ds}}{\frac{\partial{I_{ds}\left( {V_{gs},V_{ds}} \right)}}{\partial V_{d}} \cdot {\mathbb{d}V_{d}}}}}} & \left( {5.7{.1}} \right) \\ {\quad{= {{I_{dsat}\left( {V_{gs},V_{dsat}} \right)} \cdot \left\lbrack {1 + {\int_{V_{dsat}}^{V_{ds}}{\frac{1}{V_{A}} \cdot {\mathbb{d}V_{d}}}}} \right\rbrack}}} & \quad \\ {V_{A} = {I_{dsat} \cdot \left\lbrack \frac{\partial{I_{ds}\left( {V_{gs},V_{ds}} \right)}}{\partial V_{d}} \right\rbrack^{- 1}}} & \left( {5.7{.2}} \right) \end{matrix}$ Channel Length Modulation $\begin{matrix} {V_{ACLM} = {I_{dsat} \cdot \left\lbrack {\frac{\partial{I_{ds}\left( {V_{gs},V_{ds}} \right)}}{\partial L} \cdot \frac{\partial L}{\partial V_{d}}} \right\rbrack^{- 1}}} & \left( {5.7{.3}} \right) \\ {V_{ACLM} = {C_{clm} \cdot \left( {V_{ds} - V_{dsat}} \right)}} & \left( {5.7{.4}} \right) \\ {C_{clm} = {{\frac{1}{PCLM} \cdot F \cdot \left( {1 + {{PVAG}\quad\frac{V_{gsteff}}{E_{sat}L_{eff}}}} \right)}\quad\left( {1 + \frac{R_{ds} \cdot I_{dso}}{V_{dseff}}} \right){\left( {L_{eff} + \frac{V_{dsat}}{E_{sat}}} \right) \cdot \frac{1}{litl}}}} & \left( {5.7{.5}} \right) \\ {F = \frac{1}{1 + {{FPROUT} \cdot \frac{\sqrt{L_{eff}}}{V_{gsteff} + {2v_{t}}}}}} & \left( {5.7{.6}} \right) \\ {{litl} = \sqrt{\frac{ɛ_{si}{{TOXE} \cdot {XJ}}}{EPSROX}}} & \left( {5.7{.7}} \right) \end{matrix}$ Drain Induced Barrier Lower (DIBL) $\begin{matrix} {V_{ADIBL} = {I_{dsat} \cdot \left\lbrack {\frac{\partial{I_{ds}\left( {V_{gs},V_{ds}} \right)}}{\partial V_{th}} \cdot \frac{\partial V_{th}}{\partial V_{d}}} \right\rbrack^{- 1}}} & \left( {5.7{.8}} \right) \\ {V_{ADIBL} = {\frac{V_{gsteff} + {2v_{t}}}{\theta_{rout}\left( {1 + {{PDIBLCB} \cdot V_{bseff}}} \right)}\quad{\left( {1 - \frac{A_{bulk}V_{dsat}}{{A_{bulk}V_{dsat}} + V_{gsteff} + {2v_{t}}}} \right) \cdot \left( {1 + {{PVAG}\quad\frac{V_{gsteff}}{E_{sat}L_{eff}}}} \right)}}} & \left( {5.7{.9}} \right) \\ {\theta_{rout} = {\frac{PDIBLC1}{{2\quad{\cosh\left( \frac{{DROUT} \cdot L_{eff}}{lt0} \right)}} - 2} + {PDIBLC2}}} & \left( {5.7{.10}} \right) \end{matrix}$ Substrate Current Induced Body Effect (SCBE) $\begin{matrix} {I_{sub} = {\frac{A_{i}}{B_{i}}{I_{ds}\left( {V_{ds} - V_{dsat}} \right)}{\exp\left( {- \frac{B_{i} \cdot {litl}}{V_{ds} - V_{dsat}}} \right)}}} & \left( {5.7{.11}} \right) \\ {I_{ds} = {I_{{ds} - {w/o} - {Isub}} + I_{sub}}} & \left( {5.7{.12}} \right) \\ {\quad{= {I_{{ds} - {w/o} - {Isub}} \cdot \left\lbrack {1 + \frac{V_{ds} - V_{dsat}}{\frac{B_{i}}{A_{i}}{\exp\left( \frac{B_{i} \cdot {litl}}{V_{ds} - V_{dsat}} \right)}}} \right\rbrack}}} & \quad \\ {V_{ASCBE} = {\frac{B_{i}}{A_{i}}{\exp\left( \frac{B_{i} \cdot {litl}}{V_{ds} - V_{dsat}} \right)}}} & \left( {5.7{.13}} \right) \\ {\frac{1}{V_{ASCBE}} = {\frac{PSCBE2}{L_{eff}}{{\exp\left( {- \frac{{PSCBE1} \cdot {litl}}{V_{ds} - V_{dsat}}} \right)}.}}} & \left( {5.7{.14}} \right) \end{matrix}$ Drain Induced Threshold Shift (DITS) $\begin{matrix} {V_{ADITS} = {\frac{1}{PDITS} \cdot F \cdot \left\lbrack {1 + {\left( {1 + {{PDITSL} \cdot L_{eff}}} \right){\exp\left( {{PDITSD} \cdot V_{ds}} \right)}}} \right\rbrack}} & \left( {5.7{.15}} \right) \end{matrix}$ Single Equation Channel Current Model $\begin{matrix} {I_{ds} = {{\frac{I_{ds0} \cdot {NF}}{1 + \frac{R_{ds}I_{ds0}}{V_{dseff}}}\left\lbrack {1 + {\frac{1}{C_{clm}}{\ln\left( \frac{V_{A}}{V_{Asat}} \right)}}} \right\rbrack} \cdot \left( {1 + \frac{V_{ds} - V_{dseff}}{V_{ADIBL}}} \right) \cdot \left( {1 + \frac{V_{ds} - V_{dseff}}{V_{ADITS}}} \right) \cdot \left( {1 + \frac{V_{ds} - V_{dseff}}{V_{ASCBE}}} \right)}} & \left( {5.8{.1}} \right) \end{matrix}$ where NF is the number of device fingers, and V_(A) is written as  (5.8.2) V _(A) =V _(Asat) +V _(ACLM)  (5.8.3) $\begin{matrix} {V_{A}\quad{is}\quad{written}\quad{as}} & \left( {5.8{.2}} \right) \\ {V_{A} = {V_{Asat} + V_{ACLM}}} & \left( {5.8{.3}} \right) \\ {V_{Asat} = \frac{\begin{matrix} {{E_{sat}L_{eff}} + V_{dsat} +} \\ {2R_{ds}{vsatC}_{oxe}W_{eff}{V_{gsteff} \cdot \left\lfloor {1 - \frac{A_{bulk}V_{dsat}}{2\left( {V_{gsteff} + {2v_{t}}} \right)}} \right\rfloor}} \end{matrix}}{{R_{ds}{vsatC}_{oxe}W_{eff}A_{bulk}} - 1 + \frac{2}{\lambda}}} & \left( {5.8{.4}} \right) \end{matrix}$ Body Current Model

Iii Model $\begin{matrix} \begin{matrix} {I_{u} = {\frac{{ALPHA0} + {{ALPHA1} \cdot L_{eff}}}{L_{eff}}\left( {V_{ds} - V_{dseff}} \right)\exp}} \\ {\left( \frac{BETA0}{V_{ds} - V_{dseff}} \right) \cdot I_{dsNoSCBE}} \end{matrix} & \left( {6.1{.1}} \right) \\ \begin{matrix} {I_{dsNoSCBE} = {{\frac{I_{ds0} \cdot {NF}}{1 + \frac{R_{ds}I_{ds0}}{V_{dseff}}}\left\lbrack {1 + {\frac{1}{C_{clm}}{\ln\left( \frac{V_{A}}{V_{Asat}} \right)}}} \right\rbrack} \cdot}} \\ {\left( {1 + \frac{V_{ds} - V_{dseff}}{V_{ADIBL}}} \right) \cdot \left( {1 + \frac{V_{ds} - V_{dseff}}{V_{ADITS}}} \right)} \end{matrix} & \left( {6.1{.2}} \right) \end{matrix}$

Igidl Model $\begin{matrix} \begin{matrix} {I_{GIDL} = {{AGIDL} \cdot W_{effCl} \cdot {Nf} \cdot \frac{V_{ds} - V_{gse} - {EGIDL}}{3 \cdot T_{oxe}} \cdot}} \\ {{\exp\left( {- \frac{3 \cdot T_{oxe} \cdot {BGIDL}}{V_{ds} - V_{gse} - {EGIDL}}} \right)} \cdot \frac{V_{db}^{3}}{{CGIDL} + V_{db}^{3}}} \end{matrix} & \left( {6.2{.1}} \right) \end{matrix}$ Intrinsic Capacitance Modeling Basic Formulation $\begin{matrix} \left\{ \begin{matrix} \begin{matrix} {Q_{g} = {- \left( {Q_{sub} + Q_{inv} + Q_{acc}} \right)}} \\ {Q_{b} = {Q_{acc} + Q_{sub}}} \end{matrix} \\ {Q_{inv} = {Q_{s} + Q_{d}}} \end{matrix} \right. & \left( {7.2{.1}} \right) \\ {Q_{g} = {- \left( {Q_{inv} + Q_{acc} + Q_{sub0} + {\delta\quad Q_{sub}}} \right)}} & \left( {7.2{.2}} \right) \\ {{V_{th}(y)} = {{V_{th}(0)} + {\left( {A_{built} - 1} \right)V_{y}}}} & \left( {7.2{.3}} \right) \\ \left\{ \begin{matrix} {Q_{c} = {{W_{active}{\int_{0}^{L_{active}}{q_{c}{\mathbb{d}y}}}} = {{- W_{active}}C_{oxe}{\int_{0}^{L_{active}}{\left( {V_{gt} - {A_{bulk}V_{y}}} \right){\mathbb{d}y}}}}}} \\ {Q_{g} = {{W_{active}{\int_{0}^{L_{active}}{q_{g}{\mathbb{d}y}}}} = {W_{active}C_{oxe}{\int_{0}^{L_{active}}{\left( {V_{gt} + V_{th} - V_{FB} - \Phi_{s} - V_{y}} \right){\mathbb{d}y}}}}}} \\ {Q_{b} = {{W_{active}{\int_{0}^{L_{active}}{q_{b}{\mathbb{d}y}}}} = {{- W_{active}}C_{oxe}{\int_{0}^{L_{active}}{\left( {V_{th} - V_{FB} - \Phi_{s} + {\left( {A_{bulk} - 1} \right)V_{y}}} \right){\mathbb{d}y}}}}}} \end{matrix} \right. & \left( {7.2{.4}} \right) \end{matrix}$

-   -   where V_(gt)=V_(gse)−V_(th) and ${dy} = \frac{{dV}_{y}}{E_{y}}$         $\begin{matrix}         \begin{matrix}         {I_{ds} = {\frac{W_{active}\mu_{eff}C_{oxe}}{L_{active}}\left( {V_{gt} - {\frac{A_{bulk}}{2}V_{ds}}} \right)V_{ds}}} \\         {= {W_{active}\mu_{eff}{C_{oxe}\left( {V_{gt} - {A_{bulk}V_{y}}} \right)}E_{y}}}         \end{matrix} & \left( {7.2{.5}} \right) \\         {C_{ij} = \frac{\partial Q_{i}}{\partial V_{j}}} & \left( {7.2{.6}} \right)         \end{matrix}$         where i and j denote the transistor terminals, C_(ij) satisfies         ${\sum\limits_{i}\quad C_{ij}} = {{\sum\limits_{j}\quad C_{ij}} = 0}$         Short Channel Model $\begin{matrix}         {\left. {V_{{dsat},{IV}} < V_{{dsat},{CV}} < V_{{dsat},{IV}}} \right|_{{Lactive}->\infty} = \frac{V_{{gsteff},{CV}}}{A_{bulk}}} & \left( {7.2{.7}} \right) \\         {V_{{dsat},{CV}} = \frac{V_{{gsteff},{CV}}}{A_{bulk} \cdot \left\lbrack {1 + \left( \frac{CLC}{L_{active}} \right)^{CLE}} \right\rbrack}} & \left( {7.2{.8}} \right) \\         \begin{matrix}         {V_{{gsteff},{CV}} = {{NOFF} \cdot {nv}_{t} \cdot}} \\         {\ln\left\lbrack {1 + {\exp\left( \frac{V_{gse} - V_{th} - {VOFFCV}}{{NOFF} \cdot {nv}_{t}} \right)}} \right\rbrack}         \end{matrix} & \left( {7.2{.9}} \right) \\         {\begin{matrix}         {A_{bulk} = \left\{ {1 + {{F\_ doping} \cdot}} \right.} \\         \left. {\left\lbrack {\frac{{A0} \cdot L_{eff}}{L_{eff} + {2\sqrt{{XJ} \cdot X_{dep}}}} \cdot {+ \frac{B0}{W_{eff}^{\prime} + {B1}}}} \right\rbrack \cdot} \right\} \\         {\frac{1}{1 + {{KETA} \cdot V_{bseff}}}}         \end{matrix}{where}{{\begin{matrix}         {{F\_ doping} = {\frac{\sqrt{1 + {{LPEB}/L_{eff}}}K_{1{ox}}}{2\sqrt{\Phi_{s} - V_{bseff}}} +}} \\         {{K3B}\frac{TOXE}{W_{eff}^{\prime} + {W0}}\Phi_{s}}         \end{matrix}K_{2{ox}}} -}} & \left( {7.2{.10}} \right)         \end{matrix}$         Single Equation Formulation     -   depletion to inversion region $\begin{matrix}         {{Q\left( V_{gst} \right)} = {Q\left( V_{{gsteff},{CV}} \right)}} & \left( {7.2{.11}} \right) \\         {{C\left( V_{gst} \right)} = {{C\left( V_{{gsteff},{CV}} \right)}\frac{\partial V_{{gsteff},{CV}}}{V_{g,d,s,b}}}} & \left( {7.2{.12}} \right)         \end{matrix}$         Accumulation to Depletion Region $\begin{matrix}         \begin{matrix}         {V_{FBeff} = {V_{fbzb} - {0.5\left\lbrack {\left( {V_{fbzb} - V_{gb} - 0.02} \right) +} \right.}}} \\         \left. \sqrt{\left( {V_{fbzb} - V_{gb} - 0.02} \right)^{2} + {0.08V_{fbzb}}} \right\rbrack         \end{matrix} & \left( {7.2{.13}} \right)         \end{matrix}$  V _(fbzb) =V _(th)|_(zeroV) _(bs) _(andV) _(ds)         −Φ_(s) −K1{square root}{square root over (Φ_(s))}  (7.2.14)         Linear to Saturation Region $\begin{matrix}         {{V_{coeff} = {{V_{{dsat},{CV}} - {0.5\left\{ {V_{4} + \sqrt{V_{4}^{2} + {4\delta_{4}V_{{dsat},{CV}}}}} \right\}\quad\text{where}\quad V_{4}}} = {V_{{dsat},{CV}} - V_{ds} - \delta_{4}}}};{\delta_{4} = {0.02V}}} & \left( {7.2{.15}} \right)         \end{matrix}$         Charge Petitioning $\begin{matrix}         \left\{ \begin{matrix}         {Q_{s} = {W_{active}{\int_{0}^{L_{active}}{{q_{c}\left( {I - \frac{y}{L_{active}}} \right)}{\mathbb{d}y}}}}} \\         {Q_{d} = {W_{active}{\int_{0}^{L_{active}}{q_{c}\frac{y}{L_{active}}{\mathbb{d}y}}}}}         \end{matrix} \right. & \left( {7.2{.16}} \right)         \end{matrix}$         Charge—Thickness Capacitance Model $\begin{matrix}         {C_{oxeff} = \frac{C_{oxe} \cdot C_{cen}}{C_{oxe} + C_{cen}}} & \left( {7.3{.1}} \right)         \end{matrix}$     -   where         C _(cen)=ε_(si) /X _(DC)         Accumulation and Depletion $\begin{matrix}         \begin{matrix}         {X_{DC} = {\frac{1}{3}L_{debye}}} \\         {\exp\left\lbrack {{ACDE} \cdot \left( \frac{NDEP}{2 \times 10^{16}} \right)^{- 0.25} \cdot \frac{V_{gse} - V_{bseff} - V_{FBeff}}{TOXE}} \right\rbrack}         \end{matrix} & \left( {7.3{.2}} \right)         \end{matrix}$     -   where L_(debye) is Debye length, and X_(DC) is in the unit of cm         and (V_(gse)−V_(bseff)−V_(FBeff))/TOXE is in units of MV/Cm. For         numerical statbility, (7.3.2) is replaced by (7.3.3)         $\begin{matrix}         {X_{DC} = {X_{\max} - {\frac{1}{2}\left( {X_{0} + \sqrt{X_{0}^{2} + {4\delta_{x}X_{\max}}}} \right)}}} & \left( {7.3{.3}} \right)         \end{matrix}$         where         X ₀ =X _(max) −X _(DC)−δ_(x)         and X_(max)=L_(debye)/3; δ_(x)=10⁻³TOXE.         Inversion Charge $\begin{matrix}         {X_{DC} = \frac{1.9 \times 10^{- 9}\quad{cm}}{1 + \left( \frac{V_{gsteff} + {4\left( {{VTH0} - {VFB} - \Phi_{s}} \right)}}{2{TOXP}} \right)^{0.7}}} & \left( {7.3{.5}} \right)         \end{matrix}$         Body Charge Thickness in Inversion $\begin{matrix}         {\varphi_{\delta} = {{\Phi_{s} - {2\quad\Phi_{B}}} = {v_{t}{\ln\left( \frac{V_{gsteffCV} \cdot \left( {V_{gsteffCV} + {2K_{1{ox}}\sqrt{2\quad\Phi_{B}}}} \right.}{{{MOIN} \cdot K_{1{ox}}^{2}}v_{t}} \right)}}}} & \left( {7.3{.5}} \right)         \end{matrix}$  q _(inv) =−C _(oseff)·(V         _(gseff,CV)−φ_(δ))  (7.3.6)         Intrinsic Capacitance Model Equations

Accumulation Region Q _(δ) =W _(active) L _(active) C _(oxe)(V _(gs) −V _(bs) −VFBCV) Q _(sub) =−Q _(s) Q _(inv)=0

Subthreshold Region $\begin{matrix} {Q_{sub0} = {{- W_{active}}L_{active}{C_{oxe} \cdot}}} \\ {\frac{K_{1{ox}}^{2}}{2}\left( {{- 1} + \sqrt{1 + \frac{4\left( {V_{gs} - {VFBCV} - V_{bs}} \right)}{K_{1{ox}}^{2}}}} \right)} \end{matrix}$ Q_(g) = −Q_(sub0) Q_(inv) = 0

Strong Inversion Region $V_{{dsat},{cv}} = \frac{V_{gs} - V_{th}}{A_{bulk}^{\prime}}$ $A_{bulk}^{\prime} = {A_{bulk}\left( {1 + \left( \frac{CLC}{L_{eff}} \right)^{CLE}} \right)}$ $V_{th} = {{VFBCV} + \Phi_{s} + {K_{1{ox}}\sqrt{\Phi_{s} - V_{bseff}}}}$  V _(th) =VFBCV+φ _(s) +K _(lox){square root}{square root over (Φ_(s) −V _(bseff))}

Linear Region $\begin{matrix} {Q_{g} = {C_{oxe}W_{active}L_{active}}} \\ {\left( {V_{gs} - {VFBCV} - \Phi_{s} - \frac{V_{ds}}{2} + \frac{A_{bulk}^{\prime}V_{ds}^{2}}{12\left( {V_{gs} - V_{th} - \frac{A_{bulk}^{\prime}V_{ds}}{2}} \right)}} \right)} \end{matrix}$ $\begin{matrix} {Q_{b} = {C_{oxe}W_{active}{L_{active}\left( {{VFBCV} - V_{th} - \Phi_{s} -} \right.}}} \\ \left. {\frac{\left( {1 - A_{bulk}^{\prime}} \right)V_{ds}}{2} - \frac{\left( {1 - A_{bulk}^{\prime}} \right)A_{bulk}^{\prime}V_{ds}^{2}}{12\left( {V_{gs} - V_{th} - \frac{A_{bulk}^{\prime}V_{ds}}{2}} \right)}} \right) \end{matrix}$

50/50 Partitioning: $\begin{matrix} {Q_{inv} = {{- C_{oxe}}W_{active}L_{active}}} \\ {\left\{ {V_{gs} - V_{th} - \Phi_{s} - \frac{A_{bulk}^{\prime}V_{ds}}{2} + \frac{A_{bulk}^{\prime 2}V_{ds}^{2}}{12\left( {V_{gs} - V_{th} - \frac{A_{bulk}^{\prime}V_{ds}}{2}} \right)}} \right)} \end{matrix}$ Q_(s) = Q_(d) = 0.5Q_(inv)  Q _(s) =Q _(d)=0.5Q _(inv)

40/60 Partitioning: $\begin{matrix} {Q_{d} = {{- C_{oxe}}W_{active}L_{active}}} \\ {\left( {\frac{V_{gs} - V_{th}}{2} - \frac{A_{bulk}^{\prime}V_{ds}}{2} +} \right.} \\ \left. \frac{A_{bulk}^{\prime}{V_{ds}\left\lbrack {\frac{\left( {V_{gs} - V_{th}} \right)^{2}}{6} - \frac{A_{bulk}^{\prime}{V_{ds}\left( {V_{gs} - V_{th}} \right)}}{8} + \frac{\left( {A_{bulk}^{\prime}V_{ds}} \right)^{2}}{40}} \right\rbrack}}{12\left( {V_{gs} - V_{th} - \frac{A_{bulk}^{\prime}V_{ds}}{2}} \right)^{2}} \right) \end{matrix}$ Q_(s) = −(Q_(g) + Q_(b) + Q_(d))  Q _(s)=−(Q _(s) +Q _(b) +Q _(d))

0/100 Partitioning: $Q_{d} = {{- C_{oxe}}W_{active}{L_{active}\left( {\frac{V_{gs} - V_{th}}{2} + \frac{A_{bulk}^{\prime}V_{ds}}{4} - \frac{\left( {A_{bulk}^{\prime}V_{ds}} \right)^{2}}{24}} \right)}}$ Q_(s) = −(Q_(g) + Q_(b) + Q_(d))  Q _(s)=−(Q _(g) +Q _(b) +Q _(d))

Saturation Region $Q_{g} = {C_{oxe}W_{active}{L_{active}\left( {V_{gs} - {VFBCV} - \Phi_{s} - \frac{V_{dsat}}{3}} \right)}}$ $Q_{b} = {{- C_{oxe}}W_{active}{L_{active}\left( {{VFBCV} + \Phi_{s} - V_{th} + \frac{\left( {1 - A_{bulk}^{\prime}} \right)V_{dsat}}{3}} \right)}}$

50/50 Partitioning: $Q_{s} = {Q_{d} = {{- \frac{1}{3}}C_{axe}W_{active}{L_{active}\left( {V_{gs} - V_{th}} \right)}}}$

40/60 Partitioning: $Q_{d} = {{- \frac{4}{15}}C_{axe}W_{active}{L_{active}\left( {V_{gs} - V_{th}} \right)}}$  Q _(s)=−(Q _(g) +Q _(b) +Q _(d))

0/100 Partitioning: Q _(d)=0 Q _(s)=−(Q _(g) +Q _(b)) capMod=1 Q _(g)=−(Q _(inv) +Q _(acc) +Q _(sub0) +δQ _(sub)) Q _(b)=−(Q _(acc) +Q _(sub0) +δQ _(sub)) Q _(inv) =Q _(s) +Q _(d) Q _(acc) =−W _(active) L _(active) C _(oxe)·(V _(FBeff) −V _(fbzb)) Q_(g) = −(Q_(inv) + Q_(acc) + Q_(sub0) + δ  Q_(sub)) Q_(b) = −(Q_(acc) + Q_(sub0) + δ  Q_(sub)) Q_(inv) = Q_(s) + Q_(d) Q_(acc) = −W_(active)L_(active)C_(oxe) ⋅ (V_(FBeff) − V_(fbzb)) $Q_{sub0} = {{- W_{active}}L_{active}{C_{oxe} \cdot \frac{K_{1{ox}}^{2}}{2} \cdot \left\lbrack {{- 1} + \sqrt{1 + \frac{4\left( {V_{gse} - V_{FBeff} - V_{gsteff} - V_{bseff}} \right)}{K_{1{ox}}^{2}}}} \right\rbrack}}$ ${V_{{dsat},{cv}} = \frac{V_{gsteffcv}}{A_{bulk}}},{Q_{inv} = {{- W_{active}}L_{active}{C_{oxe} \cdot \left\lbrack {V_{{gsteff},{cv}} - {\frac{1}{2}A_{bulk}^{\prime}V_{cveff}} + \frac{A_{bulk}^{\prime 2}V_{cveff}^{2}}{12 \cdot \left( {V_{{gsteff},{cv}} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)}} \right\rbrack}}}$ ${\delta\quad Q_{sub}} = {W_{active}L_{active}{C_{oxe} \cdot \left\lbrack {{\frac{1 - A_{bulk}^{\prime}}{2}V_{cveff}} - \frac{{\left( {1 - A_{bulk}^{\prime}} \right) \cdot A_{bulk}^{\prime}}V_{cveff}^{2}}{12 \cdot \left( {V_{{gsteff},{cv}} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)}} \right\rbrack}}$

50/50 Charge Partitioning: $Q_{S} = {Q_{D} = {- {\frac{W_{active}L_{active}C_{oxe}}{2}\left\lbrack \quad{V_{{gsteff},{cv}} - {\frac{1}{2}A_{bulk}^{\prime}V_{cveff}} + \frac{A_{bulk}^{\prime 2}V_{cveff}^{2}}{12 \cdot \left( {V_{gsteff} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)}} \right\rbrack}}}$

40/60 Charge Partitioning: $Q_{S} = {- {\frac{W_{active}L_{active}C_{oxe}}{2\left( {V_{{gsteff},{cv}} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)^{2}}\quad\left\lbrack \quad\begin{matrix} {V_{{gsteff},{cv}}^{3} - {\frac{4}{3}V_{{gsteff},{cv}}^{2}A_{bulk}^{\prime}V_{cveff}} +} \\ {{\frac{2}{3}{V_{{gsteff},{cv}}\left( {A_{bulk}^{\prime}V_{cveff}} \right)}^{2}} - {\frac{2}{15}\left( {A_{bulk}^{\prime}V_{cveff}} \right)^{3}}} \end{matrix}\quad \right\rbrack}}$ $Q_{D} = {- {\frac{W_{active}L_{active}C_{oxe}}{2\left( {V_{{gsteff},{cv}} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)^{2}}\quad\left\lbrack \quad\begin{matrix} {V_{{gsteff},{cv}}^{3} - {\frac{5}{3}V_{{gsteff},{cv}}^{2}A_{bulk}^{\prime}V_{cveff}} +} \\ {{V_{{gsteff},{cv}}\left( {A_{bulk}^{\prime}V_{cveff}} \right)}^{2} - {\frac{1}{5}\left( {A_{bulk}^{\prime}V_{cveff}} \right)^{3}}} \end{matrix}\quad \right\rbrack}}$

0/100 Charge Partitioning: $Q_{S} = {{- \frac{W_{active}L_{active}C_{oxe}}{2}} \cdot \quad\left\lbrack \quad\begin{matrix} {V_{{gsteff},{cv}}^{3} + {\frac{1}{2}A_{bulk}^{\prime}V_{cveff}} -} \\ \frac{A_{bulk}^{\prime 2}V_{cveff}^{2}}{12 \cdot \left( {V_{{gsteff},{cv}} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)} \end{matrix}\quad \right\rbrack}$ $Q_{D} = {{- \frac{W_{active}L_{active}C_{oxe}}{2}} \cdot \quad\left\lbrack \quad\begin{matrix} {V_{{gsteff},{cv}}^{3} - {\frac{3}{2}A_{bulk}^{\prime}V_{cveff}} +} \\ \frac{A_{bulk}^{\prime 2}V_{cveff}^{2}}{4 \cdot \left( {V_{{gsteff},{cv}} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)} \end{matrix}\quad \right\rbrack}$ capMod=2 Q_(ace) = W_(active)L_(active)C_(oxeff) ⋅ V_(gbacc) $V_{gbacc} = {\frac{1}{2} \cdot \left\lbrack {V_{0} + \sqrt{V_{0}^{2} + {0.08V_{fbzb}}}} \right\rbrack}$ V₀ = V_(fbzb) + V_(bseff) − V_(gs) − 0.02 $V_{cveff} = {V_{dsat} - {\frac{1}{2} \cdot \left( {V_{1} + \sqrt{V_{1}^{2} + {0.08V_{dsat}}}} \right)}}$ V₁ = V_(dsat) − V_(ds) − 0.02 $V_{dsat} = \frac{V_{{gsteff},{cv}} - \varphi_{\delta}}{A_{bulk}^{\prime}}$ $\varphi_{\delta} = {{\Phi_{s} - {2\Phi_{B}}} = {v_{t}{\ln\left( \frac{{V_{gsteffCV} \cdot V_{gsteffCV}} + {2K_{1{ox}}\sqrt{2\Phi_{B}}}}{{{MOIN} \cdot K_{1{ox}}^{2}}v_{t}} \right)}}}$ $Q_{sub0} = {{- W_{active}}L_{active}{C_{axeff} \cdot \frac{K_{1{ox}}^{2}}{2} \cdot \left\lbrack {{- 1} + \sqrt{1 + \frac{4\left( {V_{gse} - V_{FBeff} - V_{bseffs} - V_{{gsteff},{cv}}} \right)}{K_{1{ox}}^{2}}}} \right\rbrack}}$ $Q_{inv} = {{- W_{active}}L_{active}{C_{oxeff} \cdot \left\lbrack {V_{{gsteff}.{cv}} - \varphi_{\delta} - {\frac{1}{2}A_{bulk}^{\prime}V_{cveff}} + \frac{A_{bulk}^{\prime 2}V_{cveff}^{2}}{12 \cdot \left( {V_{{gsteff},{cv}} - \varphi_{\delta} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)}} \right\rbrack}}$ ${\delta\quad Q_{sub}} = {W_{active}L_{active}{C_{axeff} \cdot \left\lbrack {{\frac{1 - A_{bulk}^{\prime}}{2}V_{cveff}} - \frac{{\left( {1 - A_{bulk}^{\prime}} \right) \cdot A_{bulk}^{\prime}}V_{cveff}^{2}}{12 \cdot \left( {V_{{gsteff},{cv}} - \varphi_{\delta} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)}} \right\rbrack}}$

50/50 Partitioning: $Q_{S} = {Q_{D} = {- {\frac{W_{active}L_{active}C_{axeff}}{2}\left\lbrack \quad{V_{{gsteff},{cv}} - \varphi_{\delta} - {\frac{1}{2}A_{bulk}^{\prime}V_{cveff}} + \frac{A_{bulk}^{\prime 2}V_{cveff}^{2}}{12 \cdot \left( {V_{{gsteff},{cv}} - \varphi_{\delta} - {A_{bulk}^{\prime}{V_{cveff}/2}}} \right)}} \right\rbrack}}}$

40/60 Partitioning: $\begin{matrix} {Q_{S} = {- \frac{W_{active}L_{active}C_{oxeff}}{2\left( {V_{{gsteff},{cv}} - \varphi_{\delta} - \frac{A_{bulk}^{\prime}V_{cveff}}{2}} \right)^{2}}}} \\ {\quad\begin{bmatrix} {\left( {V_{{gsteff},{cv}} - \varphi_{\delta}} \right)^{3} - {\frac{4}{3}\left( {V_{{gsteff},{cv}} - \varphi_{\delta}} \right)^{2}A_{bulk}^{\prime}V_{cveff}} +} \\ {{\frac{2}{3}\left( {V_{{gsteff},{cv}} - \varphi_{\delta}} \right)\left( {A_{bulk}^{\prime}V_{cveff}} \right)^{2}} - {\frac{2}{15}\left( {A_{bulk}^{\prime}V_{cveff}} \right)^{3}}} \end{bmatrix}} \\ {Q_{D} = {- \frac{W_{active}L_{active}C_{oxeff}}{2\left( {V_{{gsteff},{cv}} - \varphi_{\delta} - \frac{A_{bulk}^{\prime}V_{cveff}}{2}} \right)^{2}}}} \\ {\quad\begin{bmatrix} {\left( {V_{{gsteff},{cv}} - \varphi_{\delta}} \right)^{3} - {\frac{5}{3}\left( {V_{{gsteff},{cv}} - \varphi_{\delta}} \right)^{2}A_{bulk}^{\prime}V_{cveff}} +} \\ {{\left( {V_{{gsteff},{cv}} - \varphi_{\delta}} \right)\left( {A_{bulk}^{\prime}V_{cveff}} \right)^{2}} - {\frac{1}{5}\left( {A_{bulk}^{\prime}V_{cveff}} \right)^{3}}} \end{bmatrix}} \end{matrix}$

0/100 Partitioning: $\begin{matrix} {Q_{S} = {{- \frac{W_{active}L_{active}C_{oxeff}}{2}} \cdot \left\lbrack {V_{{gsteff},{cv}} - \varphi_{\delta} + {\frac{1}{2}A_{bulk}^{\prime}V_{cveff}} -} \right.}} \\ \left. \quad\frac{A_{bulk}^{\prime\quad 2}V_{cveff}^{2}}{12 \cdot \left( {V_{{gsteff},{cv}} - \varphi_{\delta} - \frac{A_{bulk}^{\prime}V_{cveff}}{2}} \right)} \right\rbrack \\ {Q_{D} = {{- \frac{W_{active}L_{active}C_{oxeff}}{2}} \cdot \left\lbrack {V_{{gsteff},{cv}} - \varphi_{\delta} - {\frac{3}{2}A_{bulk}^{\prime}V_{cveff}} +} \right.}} \\ \left. \quad\frac{A_{bulk}^{\prime\quad 2}V_{cveff}^{2}}{4 \cdot \left( {V_{{gsteff},{cv}} - \varphi_{\delta} - \frac{A_{bulk}^{\prime}V_{dveff}}{2}} \right)} \right\rbrack \end{matrix}$ Fringe Capacitance Model $\begin{matrix} {{CF} = {\frac{2 \cdot {EPSROX} \cdot ɛ_{0}}{\pi} \cdot {\log\left( {1 + \frac{{4.0e} - 7}{TOXE}} \right)}}} & \left( {7.5{.1}} \right) \end{matrix}$ Bias-Dependent Overlap Capacitance Model

(i) Source Side $\begin{matrix} {\frac{Q_{{overlap},s}}{W_{active}} = {{{CGSO} \cdot V_{gs}} + {{CGSL}\left( {V_{gs} - V_{{gs},{overlap}} -} \right.}}} & \left( {7.5{.2}} \right) \\ \left. \quad{\frac{CKAPPAS}{2}\left( {{- 1} + \sqrt{1 - \frac{4V_{{gs},{overlap}}}{CKAPPAS}}} \right)} \right) & \quad \\ \begin{matrix} {{V_{{gs},{overlap}} = {\frac{1}{2}\left( {V_{gs} + \delta_{1} - \sqrt{\left( {V_{gs} + \delta_{1}} \right)^{2} + {4\quad\delta_{1}}}} \right)}},} & {\delta_{1} = {0.02\quad V}} \end{matrix} & \left( {7.5{.3}} \right) \end{matrix}$

(ii) Drain Side $\begin{matrix} {\frac{Q_{{overlap},d}}{W_{active}} = {{{CGDO} \cdot V_{gd}} + {{CGDL}\left( {V_{gd} - V_{{gd},{overlap}} -} \right.}}} & \left( {7.5{.4}} \right) \\ \left. \quad{\frac{CKAPPAD}{2}\left( {{- 1} + \sqrt{1 - \frac{4V_{{gd},{overlap}}}{CKAPPAD}}} \right)} \right) & \quad \\ \begin{matrix} {{V_{{gd},{overlap}} = {\frac{1}{2}\left( {V_{gd} + \delta_{1} - \sqrt{\left( {V_{gd} + \delta_{1}} \right)^{2} + {4\quad\delta_{1}}}} \right)}},} & {\delta_{1} = {0.02\quad V}} \end{matrix} & \left( {7.5{.5}} \right) \end{matrix}$

(iii) Gate Overlap Charge Q _(overlap,g)=−(Q _(overlap,d) +Q _(overlap,s)+(CGBO·L _(active))·V _(gb))  (7.5.6) Bias-Independent Overlap Capacitance Model

The gate-to-source overlap charge is expressed by Q _(overlap,s) =W _(active) ·CGSO·V _(gs)

The gate-to-drain overlap charge is calculated by Q _(overlap,d) =W _(active) ·CGDO·V _(gd)

The gate-to-substrate overlap charge is computed by Q _(overlap,b) =L _(active) ·CGBO·V _(gb) Charge-Deficit Non-Quasi Static Model

The Transient Model $\begin{matrix} {{Q_{def}(t)} = {V_{def} \times C_{fact}}} & \left( {8.1{.1}} \right) \\ {{i_{D,G,S}(t)} = {{I_{D,G,S}({DC})} + \frac{\partial{Q_{d,g,s}(t)}}{\partial t}}} & \left( {8.1{.2}} \right) \\ {{Q_{def}(t)} = {{Q_{cheq}(t)} - {Q_{ch}(t)}}} & \left( {8.1{.3}} \right) \\ {\frac{\partial{Q_{def}(t)}}{\partial t} = {\frac{\partial{Q_{cheq}(t)}}{\partial t} - \frac{Q_{def}(t)}{\tau}}} & \left( {8.1{.4}a} \right) \\ {{\frac{\partial{Q_{d,g,s}(t)}}{\partial t} = D},G,{S_{xpart}\frac{Q_{def}(t)}{\tau}}} & \left( {8.1{.4}b} \right) \\ {\frac{1}{R_{ii}} = {{XRCRG1} \cdot \left( {\frac{I_{ds}}{V_{dseff}} + {{XRCRG2} \cdot \frac{W_{eff}\mu_{eff}C_{oxeff}k_{B}T}{q\quad L_{eff}}}} \right)}} & \left( {8.1{.5}} \right) \end{matrix}$ The AC Model $\begin{matrix} {{\Delta\quad{Q_{ch}(t)}} = \frac{\Delta\quad{Q_{cheq}(t)}}{1 + {j\quad\omega\quad\tau}}} & \left( {8.1{.6}} \right) \\ {G_{m} = {\frac{G_{m0}}{1 + {\omega^{2}\tau^{2}}} + {j\left( {- \frac{{G_{m0} \cdot \omega}\quad\tau}{1 + {\omega^{2}\tau^{2}}}} \right)}}} & \left( {8.1{.7}} \right) \\ {C_{dg} = {\frac{C_{dg0}}{1 + {\omega^{2}\tau^{2}}} + {j\left( {- \frac{{C_{dg0} \cdot \omega}\quad\tau}{1 + {\omega^{2}\tau^{2}}}} \right)}}} & \left( {8.1{.8}} \right) \end{matrix}$ Gate Electrode Electrode and Intrinsic-Input Resistance Model $\begin{matrix} {{Rgeltd} = \frac{{RSHG} \cdot \left( {{XGW} + \frac{W_{effcj}}{3 \cdot {NGCON}}} \right)}{{NGCON} \cdot \left( {L_{drawn} - {XGL}} \right) \cdot {NF}}} & \left( {8.1{.9}} \right) \end{matrix}$ Charge-Deficit Non-Quasi Static Model

The Transient Model $\begin{matrix} {{Q_{def}(t)} = {V_{def} \times C_{fact}}} & \left( {8.1{.1}} \right) \\ {{i_{D,G,S}(t)} = {{I_{D,G,S}({DC})} + \frac{\partial{Q_{d,g,s}(t)}}{\partial t}}} & \left( {8.1{.2}} \right) \\ {{Q_{def}(t)} = {{Q_{cheq}(t)} - {Q_{ch}(t)}}} & \left( {8.1{.3}} \right) \\ {\frac{\partial{Q_{def}(t)}}{\partial t} = {\frac{\partial{Q_{cheq}(t)}}{\partial t} - \frac{Q_{def}(t)}{\tau}}} & \left( {8.1{.4}a} \right) \\ {{\frac{\partial{Q_{d,g,s}(t)}}{\partial t} = D},G,{S_{xpart}\frac{Q_{def}(t)}{\tau}}} & \left( {8.1{.4}b} \right) \\ {\frac{1}{R_{ii}} = {{XRCRG1} \cdot \left( {\frac{I_{ds}}{V_{dseff}} + {{XRCRG2} \cdot \frac{W_{eff}\mu_{eff}C_{oxeff}k_{B}T}{q\quad L_{eff}}}} \right)}} & \left( {8.1{.5}} \right) \end{matrix}$ The AC Model $\begin{matrix} {{\Delta\quad{Q_{ch}(t)}} = \frac{\Delta\quad{Q_{cheq}(t)}}{1 + {j\quad\omega\quad\tau}}} & \left( {8.1{.6}} \right) \\ {G_{m} = {\frac{G_{m0}}{1 + {\omega^{2}\tau^{2}}} + {j\left( {- \frac{{G_{m0} \cdot \omega}\quad\tau}{1 + {\omega^{2}\tau^{2}}}} \right)}}} & \left( {8.1{.7}} \right) \\ {C_{dg} = {\frac{C_{dg0}}{1 + {\omega^{2}\tau^{2}}} + {j\left( {- \frac{{C_{dg0} \cdot \omega}\quad\tau}{1 + {\omega^{2}\tau^{2}}}} \right)}}} & \left( {8.1{.8}} \right) \end{matrix}$ Gate Electrode Electrode and Intrinsic-Input Resistance Model $\begin{matrix} {{Rgeltd} = \frac{{RSHG} \cdot \left( {{XGW} + \frac{W_{effci}}{3 \cdot {NGCON}}} \right)}{{NGCON} \cdot \left( {L_{drawn} - {XGL}} \right) \cdot {NF}}} & \left( {8.1{.9}} \right) \\ {{S_{id}(f)} = \frac{{KF} \cdot I_{ds}^{AF}}{C_{oxe}L_{eff}^{2}f^{EF}}} & \left( {9.1{.1}} \right) \\ {{S_{{id},{lev}}(f)} = {{\frac{k_{B}{Tq}^{2}\mu_{eff}I_{ds}}{C_{oxe}L_{eff}^{2}A_{bulk}{f^{ef} \cdot 10^{10}}}\left( {{{NOIA}\quad{\log\left( \frac{N_{0} + N^{a}}{N_{1} + N^{a}} \right)}} + {{NOIB}\left( {N_{0} - N_{1}} \right)} + {\frac{NOIC}{2}\left( {N_{0}^{2} - N_{1}^{2}} \right)}} \right)} + {\frac{k_{B}{TI}_{ds}^{2}{\Delta L}_{clm}}{{W_{eff} \cdot L_{eff}^{2}}{f^{ef} \cdot 10^{10}}} \cdot \frac{{NOLA} + {NOIBN}_{i} + {NOIGN}_{i}^{2}}{\left( {N_{i} + N^{a}} \right)^{2}}}}} & \left( {9.1{.2}} \right) \\ {N_{0} = {C_{oxe} \cdot {V_{gsteff}/q}}} & \left( {9.1{.3}} \right) \\ {N_{l} = {C_{oxe} \cdot V_{gsteff} \cdot {\left( {1 - \frac{A_{bulk}V_{dseff}}{V_{gsteff} + {2V_{i}}}} \right)/q}}} & \left( {9.1{.4}} \right) \\ {N^{a} = {k_{B}{T \cdot {\left( {{C\quad}_{oxe} + C_{d} + {CIT}} \right)/q^{2}}}}} & \left( {9.1{.5}} \right) \\ {{{\Delta L}_{clm} = {{Litl} \cdot {\log\left( \frac{\frac{V_{ils} - V_{dseff}}{Litl} + {EM}}{E_{set}} \right)}}}{E_{set} = \frac{2\quad{VSAT}}{\mu_{eff}}}} & \left( {9.1{.6}} \right) \\ {{S_{{id},{subVt}}(f)} = \frac{{{NOIA} \cdot k_{B}}{T \cdot I_{ds}^{2}}}{W_{eff}L_{eff}f^{EF}{N^{a2} \cdot 10^{10}}}} & \left( {9.1{.7}} \right) \\ {{S_{id}(f)} = \frac{{S_{{id},{lav}}(f)} \times {S_{{id},{subvt}}(f)}}{{S_{{id},{subvt}}(f)} + {S_{{{id},{lav}}\quad}(f)}}} & \left( {9.1{.8}} \right) \end{matrix}$ Channel Thermal Noise $\begin{matrix} {\overset{\_}{i_{d}^{2}} = {\frac{4k_{B}T\quad\Delta\quad f}{{R_{ds}(V)} + \frac{L_{eff}^{2}}{\mu_{eff}{Q_{inv}}}} \cdot {NTNOI}}} & \left( {9.2{.1}} \right) \\ {Q_{inv} = {W_{active}L_{active}{C_{oxeff} \cdot {NF} \cdot}}} & \left( {9.2{.2}} \right) \\ {\quad\left\lbrack {V_{gsteff} - \frac{A_{bulk}V_{dseff}}{2} + \frac{A_{bulk}^{2}V_{dseff}^{2}}{12 \cdot \left( {V_{gsteff} - \frac{A_{bulk}V_{dseff}}{2}} \right)}} \right\rbrack} & \quad \\ {\overset{\_}{v_{d}^{2}} = {4k_{B}{T \cdot \theta_{tnoi}^{2} \cdot \frac{V_{dseff}\Delta\quad f}{I_{ds}}}}} & \left( {9.2{.3}} \right) \\ {\overset{\_}{i_{d}^{2}} = {{4k_{B}T{\frac{V_{dseff}\Delta\quad f}{I_{ds}}\left\lbrack {G_{ds} + {\beta_{tnoi} \cdot \left( {G_{m} + G_{mbs}} \right)}} \right\rbrack}^{2}} -}} & \left( {9.2{.4}} \right) \\ {\quad{\overset{\_}{v_{d}^{2}} \cdot \left( {G_{m} + G_{ds} + G_{mbs}} \right)^{2}}} & \quad \\ {\theta_{tnoi} = {0.37 \cdot \left\lbrack {1 + {{TNOIB} \cdot L_{eff} \cdot \left( \frac{V_{gsteff}}{E_{sat}L_{eff}} \right)^{2}}} \right\rbrack}} & \left( {9.2{.5}} \right) \\ {\beta_{tnoi} = {0.577 \cdot \left\lbrack {1 + {{TNOIA} \cdot L_{eff} \cdot \left( \frac{V_{gsteff}}{E_{sat}L_{eff}} \right)^{2}}} \right\rbrack}} & \left( {9.2{.6}} \right) \end{matrix}$ Junction Diode IV Model

Source/Body Junction Diode

-   -   dioMod=0 $\begin{matrix}         {I_{bs} = {{{I_{sbs}\left\lbrack {{\exp\left( \frac{{qV}_{bs}}{{{NJS} \cdot k_{B}}{TNOM}} \right)} - 1} \right\rbrack} \cdot f_{breakdown}} + {V_{bs} \cdot G_{\min}}}} & \left( {10.1{.1}} \right) \\         {I_{sbs} = {{A_{seff}{J_{ss}(T)}} + {P_{seff}{J_{ssws}(T)}} + {W_{effcj} \cdot {NF} \cdot {J_{sswgs}(T)}}}} & \left( {10.1{.2}} \right) \\         {f_{breakdown} = {1 + {{XJBVS} \cdot {{\exp\left( {- \frac{q \cdot \left( {{BVS} + V_{bs}} \right)}{{{NJS} \cdot k_{B}}{TNOM}}} \right)}.}}}} & \left( {10.1{.3}} \right)         \end{matrix}$     -   dioMod=1 $\begin{matrix}         {I_{bs} = {{I_{sbs}\left\lbrack {{\exp\left( \frac{{qV}_{bs}}{{{NJS} \cdot k_{B}}{TNOM}} \right)} - 1} \right\rbrack} + {V_{bs} \cdot G_{\min}}}} & \left( {10.1{.4}} \right) \\         {I_{bs} = {{{I_{sbs}\left\lbrack {{\exp\left( \frac{{qV}_{bs}}{{{NJS} \cdot k_{B}}{TNOM}} \right)} - 1} \right\rbrack} \cdot f_{breakdown}} + {V_{bs} \cdot G_{\min}}}} & \left( {10.1{.5}} \right)         \end{matrix}$

Drain/Body Junction Diode

-   -   dioMod=0 $\begin{matrix}         {I_{bd} = {{{I_{sbd}\left\lbrack {{\exp\left( \frac{{qV}_{bd}}{{{NJD} \cdot k_{B}}{TNOM}} \right)} - 1} \right\rbrack} \cdot f_{breakdown}} +}} & \left( {10.1{.6}} \right) \\         {\quad{V_{bd} \cdot G_{\min}}} & \quad \\         {I_{sbd} = {{A_{deff}{J_{sd}(T)}} + {P_{deff}{J_{sswd}(T)}} + {W_{effcj} \cdot {NF} \cdot {J_{sswgd}(T)}}}} & \left( {10.1{.7}} \right) \\         {f_{breakdown} = {1 + {{XJBVD} \cdot {\exp\left( {- \frac{q \cdot \left( {{BVD} + V_{bd}} \right)}{{{NJD} \cdot k_{B}}{TNOM}}} \right)}}}} & \left( {10.1{.8}} \right)         \end{matrix}$     -   dioMod=1 $\begin{matrix}         {I_{bd} = {{I_{sbd}\left\lbrack {{\exp\left( \frac{{qV}_{bd}}{{{NJD} \cdot k_{B}}{TNOM}} \right)} - 1} \right\rbrack} + {V_{bd} \cdot G_{\min}}}} & \left( {10.1{.9}} \right) \\         {I_{bd} = {{{I_{sbd}\left\lbrack {{\exp\left( \frac{{qV}_{bd}}{{{NJD} \cdot k_{B}}{TNOM}} \right)} - 1} \right\rbrack} \cdot f_{breakdown}} +}} & \left( {10.1{.10}} \right) \\         {\quad{V_{bd} \cdot G_{\min}}} & \quad         \end{matrix}$         Junction Diode CV Model

Source/Body Junction Diode C _(bs) =A _(seff) C _(jbs) +P _(seff) C _(jbasw) +W _(effcj) ·NF·C _(jbsswg)  (10.2.1)

If Vbs<0, use equn. 10.2.2, otherwise use equn. 10.2.3 $\begin{matrix} {C_{jbs} = {{{CJS}(T)} \cdot \left( {1 - \frac{V_{bs}}{{PBS}(T)}} \right)^{- {MJS}}}} & \left( {10.2{.2}} \right) \\ {C_{jbs} = {{{CJS}(T)} \cdot \left( {1 + {{MJS} \cdot \frac{V_{bs}}{{PBS}(T)}}} \right)}} & \left( {10.2{.3}} \right) \end{matrix}$

If Vbs<0, use equn. 10.2.4, otherwise use equn. 10.2.5 $\begin{matrix} {C_{jbssw} = {{{CJSWS}(T)} \cdot \left( {1 - \frac{V_{bs}}{{PBSWS}(T)}} \right)^{- {MJSWS}}}} & \left( {10.2{.4}} \right) \\ {C_{jbssw} = {{{CJSWS}(T)} \cdot \left( {1 + {{MJSWS} \cdot \frac{V_{bs}}{{PBSWS}(T)}}} \right)}} & \left( {10.2{.5}} \right) \end{matrix}$

If Vbs<0, use equn. 10.2.6, otherwise use equn. 10.2.7 $\begin{matrix} {C_{jbsswg} = {{{CJSWGS}(T)} \cdot \left( {1 - \frac{V_{bs}}{{PBSWGS}(T)}} \right)^{- {MJSWGS}}}} & \left( {10.2{.6}} \right) \\ {C_{jbsswg} = {{{CJSWGS}(T)} \cdot \left( {1 - \frac{V_{bs}}{{PBSWGS}(T)}} \right)^{- {MJSWGS}}}} & \left( {10.2{.7}} \right) \end{matrix}$ Drain/Body Junction Diode C _(bd) =A _(deff) C _(jbd) +P _(deff) C _(jbdsw) +W _(effcj) ·NF·C _(jbdswg)  (10.2.8)

If Vbd<0, use equn. 10.2.9, otherwise use equn. 10.2.10 $\begin{matrix} {C_{jbd} = {{{CJD}(T)} \cdot \left( {1 - \frac{V_{bd}}{{PBD}(T)}} \right)^{- {MJD}}}} & \left( {10.2{.9}} \right) \\ {C_{jbd} = {{{CJD}(T)} \cdot \left( {1 + {{MJD} \cdot \frac{V_{bd}}{{PBD}(T)}}} \right)}} & \left( {10.2{.10}} \right) \end{matrix}$

If Vbd<0, use equn. 10.2.11, otherwise use equn. 10.2.12 $\begin{matrix} {C_{jbdsw} = {{{CJSWD}(T)} \cdot \left( {1 - \frac{V_{bd}}{{PBSWD}(T)}} \right)^{- {MJSWD}}}} & \left( {10.2{.11}} \right) \\ {C_{jbdsw} = {{{CJSWD}(T)} \cdot \left( {1 + {{MJSWD} \cdot \frac{V_{bd}}{{PBSWD}(T)}}} \right)}} & \left( {10.2{.12}} \right) \end{matrix}$

If Vbd<0, use equn. 10.2.13, otherwise use equn. 10.2.14 $\begin{matrix} {C_{jbdswg} = {{{CJSWGD}(T)} \cdot \left( {1 - \frac{V_{bd}}{{PBSWGD}(T)}} \right)^{- {MJSWGD}}}} & \left( {10.2{.13}} \right) \\ {C_{jbdswg} = {{{CJSWGD}(T)} \cdot \left( {1 + {{MJSWGD} \cdot \frac{V_{bd}}{{PBSWGD}(T)}}} \right)}} & \left( {10.2{.14}} \right) \end{matrix}$ Layout Dependent Parasitic Models

Gate Electrode Resistance $\begin{matrix} {{Rgeltd} = \frac{{RSHG} \cdot \left( {{XGW} + \frac{W_{effcj}}{3 \cdot {NGCON}}} \right)}{{NGCON} \cdot \left( {L_{drawn} - {XGL}} \right) \cdot {NF}}} & \left( {11.2{.1}} \right) \end{matrix}$ Temperature Dependence Model

-   -   -   -   -   Temperature Dependence of Threshold Voltage                     $\begin{matrix}                     \begin{matrix}                     {{V_{sh}(T)} = {{V_{th}({TNOM})} +}} \\                     {\left( {{KT1} + \frac{KT1L}{L_{eff}} + {{KT2} \cdot V_{bseff}}} \right) \cdot \left( {\frac{T}{TNOM} - 1} \right)}                     \end{matrix} & \left( {12.1{.1}} \right)                     \end{matrix}$

Temperature Dependence of Mobility U0(T)=U0(TNOM)·(T/TNOM)^(UTE)  (12.2.1) UA(T)=UA(TNOM)+UA1(T/TNOM−1)  (12.2.2) UB(T)=UB(TNOM)+UB1·(T/TNOM−1)  (12.2.3) UC(T)=UC(TNOM)+UC1·(T/TNOM−1)  (12.2.4)

Temperature Dependency of Saturation Velocity VSAT(T)=VSAT(TNOM)−AT·(T/TNOM−1)  (12.3.1)

Temperature Dependency of LDD Resistance

-   -   rdsMod=0         RDSW(T)=RDSW(TNOM)+PRT·(T/TNOM−1)  (12.4.1)         RDSWMIN(T)=RDSWMIN(TNOM)+PRT·(T/TNOM−1)  (12.4.2)     -   rdsMod=1         RDW(T)=RDW(TNOM)+PRT·(T/TNOM−1)  (12.4.3)         RDWMIN(T)=RDWMIN(TNOM)+PRT·(T/TNOM−1)  (12.4.4)         RSW(T)=RSW(TNOM)+PRT·(T/TNOM−1)  (12.4.5)         RSWMIN(T)=RSWMIN(TNOM)+PRT·(T/TNOM−1)  (12.4.6)         Temperature Dependence of Junction Diode IV         I _(sbs) =A _(seff) J _(ss)(T)+P _(seff) J _(ssws)(T)+W _(effcj)         ·NF·J _(sswgs)(T)  (12.5.1) $\begin{matrix}         {I_{sbs} = {{A_{seff}{J_{ss}(T)}} + {P_{seff}{J_{ssws}(T)}} + {W_{effcj} \cdot {NF} \cdot {J_{sswgs}(T)}}}} & \left( {12.5{.1}} \right) \\         {{J_{ss}(T)} = {{{JSS}({TNOM})} \cdot {\exp\left( \frac{\frac{E_{g}({TNOM})}{v_{t}({TNOM})} - \frac{E_{g}(T)}{v_{t}(T)} + {{XTIS} \cdot {\ln\left( \frac{T}{TNOM} \right)}}}{NJS} \right)}}} & \left( {12.5{.2}} \right) \\         {{J_{ssws}(T)} = {{{JSSWS}({TNOM})} \cdot {\exp\left( \frac{\frac{E_{g}({TNOM})}{v_{t}({TNOM})} - \frac{E_{g}(T)}{v_{t}(T)} + {{XTIS} \cdot {\ln\left( \frac{T}{TNOM} \right)}}}{NJS} \right)}}} & \left( {12.5{.3}} \right) \\         {{J_{sswgs}(T)} = {{{JSSWGS}({TNOM})} \cdot {\exp\left( \frac{\frac{E_{g}({TNOM})}{v_{t}({TNOM})} - \frac{E_{g}(T)}{v_{t}(T)} + {{XTIS} \cdot {\ln\left( \frac{T}{TNOM} \right)}}}{NJS} \right)}}} & \left( {12.5{.4}} \right)         \end{matrix}$         drain side diode         I _(sbd) =A _(deff) J _(sd)(T)+P _(deff) J _(sswd)(T)+W _(effcj)         ·NF·J _(sswgd)(T)  (12.5.5) $\begin{matrix}         {I_{sbd} = {{A_{deff}{J_{sd}(T)}} + {P_{deff}{J_{sswd}(T)}} + {W_{effcj} \cdot {NF} \cdot {J_{sswgd}(T)}}}} & \left( {12.5{.5}} \right) \\         {{J_{sd}(T)} = {{{JSD}({TNOM})} \cdot {\exp\left( \frac{\frac{E_{g}({TNOM})}{v_{t}({TNOM})} - \frac{E_{g}(T)}{v_{t}(T)} + {{XTID} \cdot {\ln\left( \frac{T}{TNOM} \right)}}}{NJD} \right)}}} & \left( {12.5{.6}} \right) \\         {{J_{sswd}(T)} = {{{JSSWD}({TNOM})} \cdot {\exp\left( \frac{\frac{E_{g}({TNOM})}{v_{t}({TNOM})} - \frac{E_{g}(T)}{v_{t}(T)} + {{XTID} \cdot {\ln\left( \frac{T}{TNOM} \right)}}}{NJD} \right)}}} & \left( {12.5{.7}} \right) \\         {{J_{sswgd}(T)} = {{{JSSWGD}({TNOM})} \cdot {\exp\left( \frac{\frac{E_{g}({TNOM})}{v_{t}({TNOM})} - \frac{E_{g}(T)}{v_{t}(T)} + {{XTID} \cdot {\ln\left( \frac{T}{TNOM} \right)}}}{NJD} \right)}}} & \left( {12.5{.8}} \right)         \end{matrix}$         Temperature Dependence of Junction Diode CV     -   source side diode         CJS(T)=CJS(TNOM)·[1+TCJ·(T−TNOM)]  (12.6.1)         CJSWS(T)=CJSWS(TNOM)+TCJSW·(T−TNOM)  (12.6.2)         CJSWGS(T)=CJSWGS(TNOM)·[1+TCJSWG·(T−TNOM)]  (12.6.3)         PBS(T)=PBS(TNOM)−TPB·(T−TNOM)  (12.6.4)         PBSWS(T)=PBSWS(TNOM)−TPBSW·(T−TNOM)  (12.6.5)         PBSWGS(T)=PBSWGS(TNOM)−TPBSWG·(T−TNOM)  (12.6.6)         drain side diode         CJD(T)=CJD(TNOM)·[1+TCJ·(T−TNOM)]  (12.6.7)         CJSWD(T)=CJSWD(TNOM)+TCJSW·(T−TNOM)  (12.6.8)         CJSWGD(T)=CJSWGD(TNOM)·[1+TCJSWG·(T−TNOM)]  (12.6.9)         PBD(T)=PBD(TNOM)−TPB·(T−TNOM)  (12.6.10)         PBSWD(T)=PBSWD(TNOM)−TPBSW·(T−TNOM)  (12.6.11)         PBSWGD(T)=PBSWGD(TNOM)−TPBSWG·(T−TNOM)  (12.6.12)         Temperature Dependences of Eg and ni         Drain Saturation Current Parameters $\begin{matrix}         {{E_{g}({TNOM})} = {1.16 - \frac{7.02 \times 10^{- 4}{TNOM}^{2}}{{TNOM} + 1108}}} & \left( {12.7{.1}} \right) \\         {{E_{g}(T)} = {1.16 - \frac{7.02 \times 10^{- 4}T^{2}}{T + 1108}}} & \left( {12.7{.2}} \right) \\         {n_{i} = {1.45e\quad{10 \cdot \frac{TNOM}{300.15} \cdot \sqrt{\frac{TNOM}{300.15}} \cdot {\exp\left\lbrack {21.5565981 - \frac{{qE}_{g}({TNOM})}{{2 \cdot k_{B}}T}} \right\rbrack}}}} & \left( {12.7{.3}} \right) \\         {{A_{bulk} = {\left\{ {1 - {\frac{\mathbb{d}V_{T,{{Long}\bot}}}{\mathbb{d}V_{{BS},{eff}}} \times \left\lbrack {{\frac{{A0} \cdot L_{eff}}{L_{eff} + {2\sqrt{{XJ} \cdot X_{dep}}}} \times \left( {1 - {{AGS} \cdot {V_{{GST},{eff}}\left( \frac{L_{eff}}{L_{eff} + {2\sqrt{{XJ} \cdot X_{dep}}}} \right)}^{2}}} \right)} + \frac{B0}{W_{eff} + {B1}}} \right\rbrack}} \right\} \times \frac{1}{1 + {{KETA} \cdot V_{{BS},{eff}}}}}}{where}{\frac{\mathbb{d}V_{T,{{Long}\bot}}}{\mathbb{d}V_{{BS},{eff}}} = {{\sqrt{1 + \frac{LPEB}{L_{eff}}} \times \frac{K1}{2\sqrt{{2\Phi_{f}} - V_{{BS},{eff}}}}\frac{TOXE}{TOXM}} + {{K2}\frac{TOXE}{TOXM}} - {{K3} \times \frac{TOXE}{W_{eff} + {W0}}2\Phi_{f}}}}} & 14.1         \end{matrix}$ 

1. A method for extracting semiconductor device model parameters, comprising: obtaining terminal current data corresponding to various bias conditions in a set of test devices; extracting V_(th) related parameters based on the terminal current data; and extracting I_(gb) related parameters based on the terminal current data and the extracted V_(th) related parameters.
 2. The method of claim 1, wherein the terminal current data comprises one or more I_(g) v. V_(bs) curves, and wherein extracting I_(gb) related parameters comprises: extracting Aigbacc, Bigbacc, and Cigbacc using non-linear square fit and the one or more I_(g) v. V_(bs) curves; and extracting Nigbacc using said extracted Aigbacc, Bigbacc, and Cigbacc and linear interpolation using maximum slope position in the one or more I_(g) vs. V_(bs) curves.
 3. The method of claim 1, wherein the terminal current data comprises one or more I_(b) v. V_(gs) curves, and wherein extracting I_(gb) related parameters comprises: extracting Aigbinv, Biginv, and Ciginv using non-linear square fit and the one or more I_(b) v. V_(gs) curves; and extracting NIgbinv and Eigbinv using the extracted Aigbinv, Bigbinv, and Cigbinv and mathematical optimization.
 4. A method for extracting semiconductor device model parameters, comprising: obtaining terminal current data corresponding to various bias conditions in a set of test devices; extracting V_(th) related parameters; and extracting I_(gidl) related parameters based on the terminal current data and the V_(th) related parameters.
 5. The method of claim 3, wherein the terminal current data comprises I_(b) v. V_(gs) curves, and wherein extracting I_(gidl) related parameters further comprises: extracting CGIDL based on the I_(b) vs V_(gs) curves for varying V_(ds); extracting AIGDL and BIGDL using non-linear square fit; and optimizing said AIGDL and said BIGDL to extract EGIDL.
 6. A method for extracting semiconductor device model parameters comprising: obtaining terminal current data corresponding to various bias conditions in a set of test devices; extracting V_(th) related parameters; and extracting I_(gd) and I_(gs) related parameters based on the terminal current data and the extracted V_(th) related parameters.
 7. The method of claim 5, wherein the terminal current data comprises I_(d) v. V_(gs) and I_(s) v. V_(gs) curves measured with V_(ds)=0 and V_(bs)=0 on one or more devices having a maximum L_(drawn)*W_(drawn) among the set of test devices, and wherein extracting I_(gc) related parameters further comprises: extracting AIGSD, BIGSD, and CIGSD using non-linear square fit method and the I_(d) v. V_(gs) and I_(s) v. V_(gs) curves.
 8. The method of claim 6, wherein extracting I_(gd) and I_(gs) related parameters further comprises: setting POXEDGE, TOXREF, and NTOX to their default values and setting DLCIG equal to 0.7 *X_(j) before extracting AIGSD, BIGSD, and CIGSD; and extracting DLCIG after extracting AIGSD, BIGSD, and CIGSD.
 9. The method of claim 5, further comprising extracting I_(gc) related parameters by: obtaining I_(g) v. V_(gs) curves for devices having a maximum L_(drawn)*W_(drawn) among the set of test devices; removing I_(gs) and I_(gd) effects from the I_(g) v V_(gs) curves using the extracted I_(gd) and I_(gs) related parameters; extracting AIGC, BIGC, and CIGC using non-linear square fit and the I_(g) v. V_(gs) curves; and extracting NIGC at V_(gs)=V_(th) using linear interpolation. and dividing I_(gc) into its two components, I_(gcs) and I_(gcd).
 10. A method for extracting semiconductor device model parameters comprising: loading measurement data; extracting V_(th) related parameters; using the extracted V_(th) related parameters to extract L_(eff), R_(d) and R_(s) related parameters; using the extracted V_(th) related parameters to extract mobility and W_(eff) related parameters; using the extracted V_(th), L_(eff), mobility, and W_(eff) related parameters to extract V_(th) geometry related parameters; using the extracted V_(th), L_(eff), R_(d) R_(s), mobility, and W_(eff) related parameters to extract sub-threshold region related parameters; using the extracted V_(th) related parameters to extract drain induced barrier lower related parameters; using the extracted V_(th), L_(eff), R_(d), R_(s), mobility, W_(eff), sub-threshold region, and drain induced barrier lower related parameters to extract I_(dsat) related parameters; and extracting additional DC related parameters.
 11. The method of claim 9, wherein the L_(eff), R_(d) and R_(s) related parameters, the V_(th) geometry related parameters, the subthreshold region related parameters, and the drain induced barrier lower related parameters are extracted using linear region I_(d) v. V_(gs) curves constructed based on the measurement data.
 12. The method of claim 9, wherein the I_(dsat) related parameters are extracted using saturation region I_(d) v. V_(ds) curves constructed based on the measurement data.
 13. The method of claim 9, wherein extracting additional DC parameters further comprises: extracting I_(ii) related parameters; and extracting junction related parameters.
 14. The method of claim 12, wherein the I_(ii) related parameters are extracted using linear region I_(d) v. V_(gs) curves constructed based on the measurement data and the junction related parameters are extracted using C_(bs) V. V_(bs) curves and C_(bd) v. V_(bs) curves constructed based on the measurement data.
 15. A method of extracting I_(gidl) related parameters for modeling a MOSFET device, comprising: obtaining terminal current data corresponding to various bias conditions in a set of test devices, the terminal current data including I_(b) vs V_(gs) curves measured on the set of test devices; extracting CGIDL using the I_(b) vs V_(gs) curves; extracting AIGDL and BIGDL using non-linear square fit; and optimizing said AIGDL and said BIGDl to extract EGIDL.
 16. A method for extracting semiconductor device model parameters comprising: obtaining terminal current data corresponding to various bias conditions in a set of test devices; extracting I_(gb) related parameters, I_(gidl) related parameters, I_(gd) and I_(gs) related parameters, and I_(gc) related parameters from the terminal current data; modifying the terminal current data using the I_(gb) related parameters, I_(gidl) related parameters, I_(gd) and I_(gs) related parameters, and I_(gc) related parameters; and extracting additional DC parameters using the modified terminal current data.
 17. The method of claim 15, wherein extracting additional DC parameters further comprises: extracting L_(eff), R_(d) and R_(s) related parameters; extracting mobility and W_(eff) related parameters; using the extracted L_(eff), mobility and W_(eff) related parameters to extract V_(th) geometry parameters; using the extracted L_(eff), R_(d) and R_(s), mobility and W_(eff) related parameters to extract sub-threshold region related parameters; extracting DIBL related parameters; and using the extracted L_(eff), R_(d) and R_(s), mobility and W_(eff) V_(th) geometry, sub-threshold region and DIBL related parameters to extract I_(dsat) related parameters
 18. The method of claim 16, wherein extracting additional DC parameters further comprising: extracting I_(ii) related parameters; and extracting junction related parameters.
 19. A computer readable medium comprising computer executable program instructions that when executed cause a digital processing system to perform a method for extracting semiconductor device model parameters, the method comprising: obtaining terminal current data corresponding to various bias conditions in a set of test devices; extracting I_(gb) related parameters, I_(gidl) related parameters, I_(gd) and I_(gs) related parameters, and I_(gc) related parameters from the terminal current data; modifying the terminal current data using the extracted I_(diode) related parameters and I_(bjt) related parameter extracting I_(gb) related parameters, I_(gidl) related parameters, I_(gd) and I_(gs) related parameters, and I_(gc) related parameters; and extracting additional DC parameters from the modified terminal current data.
 20. A system for extracting semiconductor device model parameters, comprising: a central processing unit (CPU); a port or I/O device communicating with the central processing unit to provide terminal current data to the CPU corresponding to various bias conditions in a set of test devices; a memory communicating with the CPU and storing therein program instructions executable by the CPU to extract I_(gb) related parameters, I_(gidl) related parameters, I_(gd) and I_(gs) related parameters, and I_(gc) related parameters from said terminal current data, to modify said terminal current data based on the extracted I_(gb) related parameters, I_(gidl) related parameters, I_(gd) and I_(gs) related parameters, and I_(gc) related parameters, and to extract DC parameters based on said modified terminal current data.
 21. The system according to claim 19, wherein said memory also stores program instructions executable by the CPU to: extract V_(th) related parameters; use the extracted V_(th) related parameters to extract L_(eff), R_(d) and R_(s) related parameters; use the extracted V_(th) related parameters to extract mobility and W_(eff) related parameters; use the extracted V_(th), L_(eff), R_(d), R_(s), mobility and W_(eff) related parameters to extract sub-threshold region related parameters; use the extracted V_(th) related parameters to extract drain induced barrier lower related parameters; and use the extracted V_(th), L_(eff), R_(d), R_(s), mobility, W_(eff), sub-threshold region, and drain induced barrier lower related parameters to extract I_(dsat) related parameters. 